## Debt consolidation with long-term debt

Alexander Scheer∗

This version: October 2015

Abstract

This paper assesses the dynamics of public debt and output growth following tax- vs. spending-based fiscal consolidation. A permanent reduction in debt to GDP is simulated within a model that allows for different average maturities of public debt. That latter feature is important as it shapes relative effectiveness of the two fiscal schemes in reducing debt via their induced effects on interest payments. For a long enough maturity, tax hikes reduce real interest payments while spending cuts increase them. The reverse is true if the maturity of public debt is short. Output contracts in either case, but least so for tax hikes and long average maturities. Calibrated to match US debt characteristics in 2015, tax-based consolidation is shown to be less costly in terms of output and welfare losses. Monetary policy can change this result by targeting a zero inflation rate. If the speed or amount of consolidation is low the maturity structure becomes less important.

Keywords: Consolidation, Government debt, Fiscal policy, Inflation, Maturity structure, New Keynesian models.

JEL-Codes: H63, E63

∗

University of Bonn, Adenauerallee 24-42, 53113 Bonn, Germany. Email: alexander.scheer@uni-bonn.de.

The first version is from April 2014. I thank Gernot J. M¨uller, J¨urgen von Hagen, Klaus Adam, Stefania

Albanesi, Francesco Bianchi, Filippo Brutti, Keith Kuester and Michael Kumhof for valuable comments and discussions as well as seminar participants at the MEF-Seminar in Bonn, 11th Dynare conference in Brussels, International Conference on Public Policy and Public Sector Reforms in Delphi, ifo-workshop in Dresden, 46th MMF in Durham, More Europe or More Subsidiarity? in Freiburg, 30th EEA in Mannheim, Jahrestagung

2015 in M¨unster, PhD-conferences in Thessaloniki and Warwick. I also thank the German Science Foundation

### 1

### Introduction

The Great Recession has sent government debt to GDP ratios to a post-WWII high for several advanced economies. These elevated public debt levels have raised concerns about their sustainability and revived discussions on ways of consolidation. One particular choice of policymakers is whether to raise tax rates or reduce expenditures. The empirical literature on the composition of fiscal consolidation is primarily concerned with the implied growth dynamics and possible conditions for expansionary austerity, see for instance Alesina et al. (2015) or Guajardo et al. (2014).

In this paper I highlight the importance of changes in real interest payments on government debt since this has a direct impact on the debt dynamics, next to the output growth and the primary surplus itself. For example, a reduction in interest payments c.p. decreases the debt ratio or, for a given aim of debt reduction, lowers the need to adjust fiscal instruments. This further reduces (possible) adverse affects on growth with another round of feedback effects. To assess these implications on public debt, output growth and real interest payments follow-ing a tax- vs. spendfollow-ing-based fiscal consolidation, I set up a New Keynesian model that allows for different average maturities of public debt. That latter feature is important as the induced change in the real interest payments for each of the two consolidation depends on the average maturity in place. If it is long enough, tax hikes actually reduce real interest payments while spending cuts raise them. The reverse is true if the maturity of public debt is short. The reason is twofold: First, tax hikes are inflationary whereas spending cuts deflationary. In the model, the former is captured by an increase in the labor tax rate. This increases pre-tax wages to compensate part of the loss in income which raises marginal costs and thus prices, see for instance Eggertsson (2011). The latter is modeled as a reduction in public purchases which induces firms to lower the price to attract private demand. Empirically, Alesina et al. (2015) find in their sample of consolidation periods in 16 OECD countries that this is also the case.1 Second, even though monetary policy follows the Taylor-principle, nominal interest payments on public debt react less than one-to-one since only a fraction of that debt is rolled over.

I simulate a 10% permanent reduction in the targeted debt to GDP ratio accomplished within 10 years. Fiscal policy is captured by simple feedback rules that increase (decrease) the tax rate (government spending) if the actual debt to GDP ratio is above its target rate. When the model is calibrated to US debt characteristics in 2015 it is shown that a tax-based

consolida-1

They examine in figure 8 the effect of tax- vs. spending-based consolidation on the GDP deflator. Except for Canada and Australia tax hikes increase inflation and spending cuts decrease it (are deflationary), although there is some overlapping in the confidence bands for some countries.

Canada France Germany Italy Japan UK US

6 7 5.9 6.9 6.3 15 5

Table 1: Average maturity of debt in years as in 2013. For France and Italy data is from 2010. Sources: ECB, Government Statistics, Average residual maturity of debt; OECD.Stats, Central Government Debt, Average term to maturity and duration; HM Treasury

tion is strictly preferable to a spending-based one in terms of welfare and output losses. For that, I calculate the welfare equivalent consumption variation (CV) and the “Fiscal Sacrifice Ratio” (FSR) that quantifies the output drop for a given debt reduction. The CV (including the transition) is 0.04% for the tax-based consolidation and -0.06% for the spending-based one which implies that households are better off with a consolidation undertaken by tax hikes. I assess the sensitivity of these results with respect to the average maturity to reconcile that part of the literature finds less adverse effects for spending-cuts. If government debt con-sists only of one-period debt I also find that spending cuts are indeed less costly in terms of welfare and especially output. The CV is -0.12% and -0.01% for tax- and spending-based consolidation respectively. Empirically, as table 1 illustrates for the G7, the average maturity of government debt is much larger than one period and ranges between 5 to 15 years with a mean of around 7 years. This raises to some degree doubt on the plausibility of one-period debt models for studying public debt dynamics.

The next section provides an overview of the related literature including a subsection on optimal debt levels. The model is introduced in section 3. Section 4 shows the long-run implications and section 5 the corresponding transitions towards the long-run. Some impli-cations of the model and future research is laid out in section 6 before section 7 concludes.

### 2

### Literature review

2.1 Consolidation

As emphasized above, the question of how and when to reduce government debt is at the heart of consolidation debates.

The timing-dimension is quite controversial: Gros (2011), Holland and Portes (2012) and Krugman (2010) argue that austerity in recessions can become self-defeating in the sense that the resulting drop in economic activity actually leads to increased debt ratios. However, M¨uller (2014) shows that in times of fiscal stress this seems to be rather unlikely.2 Addi-tionally, Auerbach and Gorodnichenko (2012) do not find much output response to spending

2

The two conditions needed are high public debt levels and a monetary policy that is constrained by the zero lower bound.

shocks once they control for high debt levels.

Most of the theoretical literature on different consolidation-instruments finds that revenue-increasing measures tend to have larger adverse effects on output if monetary policy is uncon-strained, see for instance Coenen et al. (2008), Forni et al. (2010) or Erceg and Lind´e (2013). The first two studies are method-wise very close to this thesis. Coenen et al. (2008) use a two-country open-economy model of the euro area to evaluate the macroeconomic consequences of various fiscal consolidation schemes. They find positive long-run effects on output and consumption combined with considerable short-run adjustment costs and possibly distribu-tional effects. However, they do not pose a clear metric like the FSR or CV that guide the reader on how to compare the various instruments. Forni et al. (2010) have a more detailed description of the public sector and show that a 10 percentage point reduction of the debt to GDP ratio obtained by reducing expenditure and taxes can be welfare improving. Erceg and Lind´e (2013) use a medium scaled two-country DSGE model to compare the effects of tax- vs. expenditure-based fiscal consolidation with different degrees of monetary policy accommoda-tion. With an independent central bank, government spending-cuts are less costly in reducing public debt than tax-hikes. The reason is that potential output falls relatively more when taxes are raised while spending-cuts can partially accommodated by a cut in the policy rate that crowds-in private demand. In a currency union, however, the central bank provides too little accommodation as it focuses on union-wide aggregates only. Therefore, expenditure-based consolidation depresses output by more in the short run. A currency union seems to strengthen my mechanism as well: as emphasized above, increases in the labor tax rate re-duce total financing costs in real terms, although for a small fraction that is reissued, the government has to pay a higher nominal rate. If the monetary authority would react less strongly to the inflation rate, as in the case of a monetary union, the short-term rate would be relatively lower which, all else equal, further reduces total financing costs. This enhances the relative advantage of tax-hikes compared to spending-cuts, as for the latter, by the same argument, the increase in financing costs would be even stronger. One particular drawback of the three studies above is that they study New Keynesian models with one period debt which shuts down the above emphasized mechanism.

Another aspect of importance for the macroeconomic impacts of fiscal consolidation is a pos-sible uncertainty of the timing (at which debt levels to consolidate) and the composition (expecting a raise in taxes but a reduction in spending realize). To study those consequences, Bi et al. (2013) set up a New Keynesian model with short-term debt and show the conditions under which in such an environment stabilizing government debt will be successful. Interest-ingly, most of their arguments rest on the above laid-out mechanism that in a model with

short-term debt, tax-hikes (spending-cuts) increase (decrease) the inflation rate and thus the short-term financing costs. In a similar vein, Romei (2014) argues that spending-based consol-idation is preferable in a New Keynesian Model with heterogeneous agents where households can vote for each policy option. She argues that it is especially preferable to have lower fi-nancing costs when consolidation takes place which is the case by spending-cuts. It would be interesting to see how the introduction of long-term debt affects the results in both papers as the change in the financing costs of the whole bond-portfolio is much more muted compared to short-term debt.

The empirical literature on the composition of fiscal consolidations seems to be leaning more towards less disruptive effects of expenditure-based measures. This view has been put forward by Alesina and Perotti (1995) and the more recent study by Alesina and Ardagna (2010), although their methodology has not been unchallenged, see Jayadev and Konczal (2010) or Guajardo et al. (2014). Alesina et al. (2015) show that the result of less disruptive effects of spending holds true when using a different methodology and considering fiscal plans rather than one-time shocks. While the reason they put forward is that business confidence is af-fected adversely when taxes increase which has a strong dampening effect, Guajardo et al. (2014) argue that this is due to different monetary policy responses. However, in all empirical studies they do not condition on the maturity, the amount of consolidation, whether debt was reduced after all and the economic circumstances - all ingredients which in the model are important. In fact, in Alesina et al. (2015) the average and the median change in debt to GDP actually increases during consolidation periods. Holden and Midthjell (2013) show that the success of reducing debt is not determined by the fiscal instrument but rather whether the adjustment was sufficiently large.

In terms of an empirical (successful) debt reduction, Hall and Sargent (2011) document that in the US after WWII, most of the debt was reduced by steady positive GDP growth rates. They use a detailed accounting scheme to assess the contribution of growth, primary surpluses and real interest rates on the debt level. As growth is not a direct policy option (at least in the short run) I focus on changes of primary surpluses and do not consider direct default nor to inflate debt away as both instruments might entail tremendous costs.3

2.2 Optimal debt levels

The motivation for consolidation periods is that current debt levels are above some optimal debt to GDP ratio. There is quite an elaborate literature which covers a wide range of possibilities: debt can be either indeterminate, positive or negative. Barro (1979) shows in a

3

See for instance Barro and Gordon (1983) or, more recently, Roubini (2011) on why inflation is neither desirable nor likely to reduce debt.

simple framework that it is optimal to keep marginal tax rates constant to reduce distortions. This results in a unit root for debt which makes up part of the financing need. Aiyagari et al. (2002) formalized that approach in a Ramsey model, however, they find that debt optimally is negative to reduce distortions from taxes. In Aiyagari and McGrattan (1998) government debt increases the liquidity of agents in an incomplete markets setup and allows for more consumption smoothing which raises overall welfare. However, once on matches the model to a plausible wealth distribution, the optimal level is rather reduced, see R¨ohrs and Winter (2014). von Weizsaecker (2011) argues that government debt is a warranty, not a threat, for price stability as it raises the natural rate of interest which would have been negative due to demographical changes.

A number of researchers have brought attention towards possibly adverse effects of too much debt for the economy. First Reinhart and Rogoff (2010, 2013) have documented an inverse relationship between government debt and growth for elevated levels of debt.4 Second, high debt levels might give rise to the existence of a “crisis zone”, in which the probability to default is determined by beliefs of the agents, as in Cole and Kehoe (2000) or Conesa and Kehoe (2012). This provides an incentive for the government to reduce its outstanding liabilities to exit that zone. Third, high debt levels may lead to inflation as emphasized by Sargent and Wallace (1981), Woodford (1995), Cochrane (1999) or Sims (2013). In those models inflation rises in equilibrium to reduce the real amount of government debt if the fiscal authority is constrained to adjust its real primary surpluses and thus does not provide the necessary fiscal backup.

### 3

### Model set up

In this section I first describe the structural model before I continue to explain the solution method and the parameterization.

I use a closed economy New Keynesian model with the extension of long-term bonds as in Krause and Moyen (2013) augmented by fiscal policy rules. There are three agents in the economy: households that maximize their life time utility, firms that maximize profits and a government authority that sets distortionary labor tax rates and the welfare-enhancing level of public expenditures in order to keep the actual debt level close to some target rate. The household derives utility from consumption of a private and public good and from leisure. The asset market consists of a one period risk-free bond and a second market where long-term bonds can be traded. An important feature of the latter debt market is that such

4

Reinhart et al. (2012) and Panizza and Presbitero (2013) provide a comprehensive survey of empirical research on the existence and significance of thresholds and the causality of the negative relationship.

bonds mature stochastically. All households supply their labor services in a competitive labor market. On the production side there are two types of firms. The monopolistic competitive firms hire labor to produce intermediate goods and sell the goods to the final-good firm. They face nominal rigidities `a la Calvo (1983) when setting their optimal price. The final-good firm uses the intermediate goods in a constant-elasticity-of-substitution (CES) production function to produce an aggregate good `a la Dixit and Stiglitz (1977) which is sold to the households in a perfectly competitive market. The monetary authority follows a standard Taylor rule that reacts on deviations from inflation.

3.1 Long-term bonds

A central innovation compared to previous studies is the use of an extended maturity structure
for long-term bonds where I follow Krause and Moyen (2013). Each unit of such a debt
contractB_{t}L,npays an interest rate iL,n_{t} and matures next period with probabilityγ in which
case it also pays back the principal of 1. Thenstands for newly-issued debt and its interest
rate iL,n_{t} will be going to be priced according to a no arbitrage condition stemming from
the households first order conditions. Implicitly, each unitBL,n_{t} is actually a representative
portfolio of a unit-mass of long-term bonds where each bonds matures stochastically and
independently. Then, by the law of large numbers, a fractionγ actually matures each period.
It is easily shown that the average maturity is given by 1_{γ}. However, it is important to note
thatγnot only determines the average maturity but also the amount of bonds maturing every
period, see the implications below for US data. Since every period a fraction 1−γ does not
mature, the stock of long-term debtB_{t}L evolves as

B_{t}L= (1−γ)B_{t}L_{−1}+B_{t}L,n (1)

Thus, the assumption of a stochastic call date that is independent across time and bonds,
allows a recursive representation which is easily tractable. In a similar vein one can rewrite
the average interest expenses on the whole long-term bond portfolioiL_{t}BL_{t} recursively:

iL_{t}B_{t}L= (1−γ)iL_{t}−1BtL−1+iL,nt B
L,n

t (2)

Rewriting equation (2) to

iL_{t}B_{t}L=iL,n_{t} B_{t}L,n+ (1−γ)iL,n_{t}_{−1}B_{t}L,n_{−1}+ (1−γ)2iL,n_{t}_{−2}B_{t}L,n_{−2}+. . . (3)

shows that the average interest rate costs of the portfolio is a weighted sum of interest expenses
of previously issued long-term debt. Similarly one can express the average interest rate iL_{t}

as a weighted sum of previously set long-term interest rates iL,n_{t} , weighted by the relative
fraction of those bonds that did not yet mature:5

iL_{t} =iL,n_{t} B
L,n
t
B_{t}L +i
L,n
t−1(1−γ)
B_{t}L,n_{−1}
B_{t}L +i
L,n
t−2(1−γ)2
B_{t}L,n_{−2}
B_{t}L +. . . (4)

Thus, the average financing rate depends on a weighted sum of interest rates of previously issued long-term debt, which, as shown later, are a function of future expected short-term rates. This explains why long-term debt cushions the budget implications of changes in the short-term rates. An alternative approach is to use the characteristics of Woodford (2001), but the results did not change.6 Further alternative specifications can be found in Faraglia et al. (2013), Chatterjee and Eyigungor (2012) or Hatchondo and Martinez (2009), however, every approach can be easily mapped into each other by the right choice of free parameters. I used Krause and Moyen (2013) since it makes transparent which interest rates are actually of importance for the financing costs, i.e. short-term, newly issued long-term or average interest rates.

3.2 Households

Households maximize their life time utility given by

E0 ∞ X t=0 βt C1−σ 1−σ +χg G1−σg 1−σg −χn N1+φ 1 +φ subject to PtCt+Bt+BtL,n≤PtWtNt(1−τt) + (1 +it−1)Bt−1+ (γ+itL−1)BtL−1+PtDt

They earn after-tax wage income, the returns from the short- and long-term bonds and dividends from firm ownerships which they use for private consumption and investment in the bond markets. Denote with λt the Lagrange multiplier attached to the budget constraint

while µt is the multiplier of the average interest payments for the representative portfolio,

equation (2) after the amount of newly issued long term bonds from equation (1) have been substituted in.7 The representative household maximizes its life time utility by choosing

Ct, Bt, BtL, itLandNt. Note that the interest rate on newly issued long-term debtiL,nt is taken

5

I use the terms average interest rate and average financing costs interchangeably 6

In Woodford (2001) any bondblt is bought atqtland lasts forever with an exponentially decaying coupon

payment of factor ρ. However, the debt ratio is not uniquely defined in the model as it could be written

as face or market value. The former, dt = qlblt, where ql denotes the steady-state value of the bond price,

displays aggregate responses that are completely similar. The latter,dt=qltblt, changes the results completely.

However, for most countries debt is measured at face value.

7_{To arrive at the expression one has to scale}_{µ}

as given, similar to the short-term policy rate. However, the average financing costsiL_{t} depend
on the composition of newly issued and outstanding bonds and is thus be chosen indirectly
by the household.

The first order conditions for the short-term bond holdings yield the familiar Euler equation:

C_{t}−σ =βEt
1 +it
1 +πt+1
C_{t}−_{+1}σ
(5)
The optimality condition for long-term bonds is

1 =βEt
_{C}−σ
t+1
C_{t}−σ
1
1 +πt+1
h
1 +iL,n_{t} −µt+1(1−γ) iL,nt+1−i
L,n
t
i
(6)
whileµt evolves according to

µt=βEt
_{C}−σ
t+1
C_{t}−σ
1
1 +πt+1
1 + (1−γ)µt+1
. (7)

The last two equations deserve a bit more attention. Note first that (7) in steady state results
inµ= _{i}_{+}1_{γ} which is the pricing function for a one-period bond if γ = 1 and a consol ifγ = 0.
Remember that µt is the Lagrange multiplier on (2) so one can interpret it as the price of

the stochastic bond. As can be seen from equation (7) the price is higher than for short-term
debt. In case ofγ = 1 equation (6) implies iL,n_{t} =itand the second Euler equation collapses

to the first one. The two Euler equations (5) and (6) constitute the no arbitrage condition
for investing at different horizons. The right hand sight of (6) is the expected payoff of a long
term-debt valued by the stochastic discount factor. It consists of two parts, the first, 1 +iL,n_{t}

is the return if the bond would mature next period. The second, −µt+1(1−γ)(iL,n_{t}_{+1}−iL,nt ),

can be interpreted as the capital loss (gain) that arises from a rise (fall) in the newly issued
long term rate. The no arbitrage condition implies that once the household expects a rise of
newly-issued long-term interest rates, i.e. iL,n_{t}_{+1} > iL,n_{t} , he asks for a premium to compensate
the investment as it ties resources for several periods. It is optimal to take into account the
direct return plus the opportunity costs of having resources fixed in a long-term contract.
The remaining FOC yields the labor supply

Wt(1−τt) =χnNtφC σ

t. (8)

3.3 Firms

The final good firm uses intermediate goods from the monopolistic competitive firm and
produces a final good with a CES production function. Its demand for each intermediate
good j is given by
yt(j) =
P_{t}(j)
Pt
−
yd_{t}

whiley_{t}d is the household demand for a final good.

Each intermediate good firm produces its goodyt(j) according toyt(j) =AtNt(j) whileNt(j)

is the amount of labor and At aggregate technology. As the production function exhibits

constant returns to scale marginal costs are independent of the level of production and equal to

mct=

Wt

At

(9) Each firm sets a profit maximizing price subject to Calvo (1983) nominal frictions. The FOC of the firm can be cast into the following recursive forms:

g1_{t} =λtmctytd+βθEt
g1_{t}_{+1}
(10)
g_{t}2=λtydt +βθEt
g_{t}2_{+1}
(11)
while the optimal price is equal to

P_{t}∗
Pt
=
−1
g1_{t}
g2
t
. (12)

The price index evolves according to

1 =θ(1 +πt)−1+ (1−θ) P∗ t Pt 1− . (13) 3.4 Government

Fiscal policy is captured by simple feedback rules that increase (decrease) the tax rate (gov-ernment spending) if the actual debt to GDP ratio is above some target ratio ¯dt. The latter

will be reduced exogenously to a lower value ¯dnew < d¯old which summarizes the desire to reduce debt levels permanently. Furthermore, it seems plausible that policymakers plan to reduce the target ratio gradually to avoid potentially large adverse consequences on output. To capture this gradualism I follow Coenen et al. (2008) and use the following law of motion:

¯

dt= (1−ρd) ¯dnew+ρbd¯t−1 (14)

whereρd is chosen such that the debt to GDP target converges to its new level of ¯dnew after

approximately 40 quarters. The government budget constraint is given by

Bt+BtL,n+PtτtWtNt=PtGt+ (1 +it−1)Bt−1+ (γ+iL_{t}−1)BtL−1 (15)

which states that the government finances its public expenditures and interest payments with tax revenues or the issuance of new debt. Fiscal rules will react on the difference between the

debt ratio and its respective target ¯dt. I define the debt to GDP ratio in the model by

dt=

B_{t}L+Bt

4Ynew (16)

but one could similarly have defined the ratio with respect to the actual GDP dt = B L

t+Bt

4Yt ,

the overall picture does not change qualitatively. 3.4.1 Tax consolidation

If consolidation is achieved by increases in the tax rate, the fiscal feedback rule is given by

τt−τnew= φτ

|{z}

>0

(dt−d¯t). (17a)

Note that the fiscal rule is in deviation from the new steady state tax rateτnew_{that is }

consis-tent with the lower debt level ¯dnew. The parameterφτ captures the pace of adjustment, the

larger its value the stronger taxes react on deviations from the target. As will be explained in detail in the next section, the new steady state implies a different amount of public expen-ditures. This enhances transparency with respect to the instruments used as the initial and the end steady state are similar. Therefore, I have to make an additional assumption on how government spending will move towards its new steady state value. However, the results are unchanged when spending is kept constant and all the free resources are used to lower taxes. I chose a similar law of motion as for the evolution of the debt ratio target, namely:

Gt= (1−ρg)Gnew+ρgGt−1 (18a)

whileρg is chosen such that Gt converges after 40 quarters toGnew.8

3.4.2 Government spending

If the consolidation is achieved through a reduction in government expenditures, the spending path evolves according to

Gt−Gnew= φg

|{z}

<0

(dt−d¯t). (17b)

Tax rates will evolve towards their new steady state value by

τt= (1−ρτ)τnew+ρττt−1. (18b)

8

I provide robustness results for different transitional specifications of exogenous transition. Overall the results are robust to linear, front loading or back-loading adjustments.

3.4.3 Monetary policy

Monetary policy is set according to a standard Taylor-rule that only reacts on the inflation
rate:9
1 +it
1 +i =
1 +π_{t}
1 +π
φπ
(19)

3.5 Aggregation and exogenous rules

Finally, the goods market must clear such that

Yt∆t=AtNt (20)
with
∆t=
Z 1
0
P_{t}(i)
Pt
−
di

and by the Calvo-property

∆t=θ∆t−1(1 +πt)+ (1−θ) P∗ t Pt − . (21)

The aggregate resource constraint is

Yt=Ct+Gt (22)

and aggregate technology evolves according to

At= (At−1)ρaeε

a

t (23)

3.6 Model calibration and solution technique

Equations (1) to (23) describe the non-linear model economy. To analyze the transition towards the new steady state I use a perfect foresight solver. In a nutshell, the algorithm finds numerical values of the variables that solve the non-linear equations. The important assumption one has to impose is that the model returns to equilibrium in finite time instead of asymptotically. Taking the labor supply (8) as an example one rewrites

Wt(1−τt) =χnNtφCtσ ⇔Wt(1−τt)−χnNtφCtσ = 0

Proceeding for equations (1) to (23) one can cast the model in timetinto

f(Xt+1, Xt, Xt−1) =f(zt) = 0

withXt={Wt, τt, Nt, Yt. . .}denoting all model variables at timetandzt= [Xt+1, Xt, Xt−1] collecting forward and backward-looking terms. One has to choose, first, a starting point

Table 2: Calibration Parameter Value Description

Preferences

β 0.99 Time discount factor

σ 1 Inter-temporal elasticity of substitution private consumption, implies log-utility

σg 1 Inter-temporal elasticity of substitution public consumption,

implies log-utility 1

φ 1 Inverse of the Frish elasticity of labor supply

χn 6.67 Weighting parameter of dis-utility of work, targetsNold= 1_{3}

χg 0.2732 Together withσg = 1 implies that optimal to spend 20% of

output on public goods Firms

6 Price markup of 20%

θ 0.75 One year price contracts Monetary policy

φπ 1.5 Response of interest rate to inflation

Fiscal policy

φτ 1.5 Ensures that debt follows target

φg -0.5 Ensures that debt follows target

ρb 0.84 Autocorrelation of debt target

Long term bonds

γ 0.055 Implies maturity of 4.5 years

X0 =Xold, e.g. the initial steady state with high debt, second, an ending pointXT+1 =Xnew, the new steady state with lower debt and finally the number of periods to simulate, e.g. 2000 periods. The algorithm than stacks for t= 1,2, ...,2000 all the equations into one big system

F(Z) = 0, Z = [z1 z2 . . . zT], i.e. a system of 23*2000 equations, and solves for the root.10

Since in this theses I am interested how the maturity structure affects the macroeconomic implications of fiscal consolidation I set the amount of short-term debtBt≡ 0 for all t and

thus abstract from any portfolio decision taken by the government.11 I calibrate the model to match the debt characteristics of the US economy in 2015. The model starts with an initial debt to GDP level of 100% and a debt target of ¯dnew = 90%. γ is equal to 0.055 to match

10

This algorithm is implemented in Dynarehttp://www.dynare.org/.

11

Krause and Moyen (2013) set the real level of debt Bt_{P}

t =bt =b to a constant. However, as there is no

steady state inflation in my specification both specifications yield similar results. A complementary approach would be to choose a constant proportion of short- relative to long-term bonds. I will come back to that issue in the remark section.

2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 0.05 0.1 0.15 0.2 0.25 0.3 Year Share as of 2011

**Share of debt maturing**

Data Model

Figure 1: Fraction of debt maturing within next 10 years. The dashed line depicts the amount of debt in the US as of June 2011 that matures in years 2012 to 2021. The solid line is the corresponding fraction implied by the model. Sources: Bohn (2011).

the average maturity of US debt in 2011 of 55 months.12 The fiscal feedback rules will trigger the dynamic adjustment towards the new steady state.

The other model parameter are chosen to follow the literature for quarterly frequency. The time preference rate β is chosen to match an average annual real return of 4%. The inter-temporal elasticity of substitution of private and public goods σ, σg as well as the inverse

Frish elasticity 1_{φ} are all set to 1. In the economy there will be a steady state mark up of 20%
and the average adjustment of nominal prices will take one year, so = 6 and θ= 0.75. The
policy parameters for the Taylor rule are standard values that satisfy the Taylor principle
withφπ = 1.5. The adjustment parameters on the fiscal feedback rules were chosen such that

the actual debt level will be reduced by 10%−points within 40 quarters.

However, as emphasized above, γ also captures the average amount of debt that matures
within one quarter. Figure 1 depicts how that calibration fits the US data quite well. I set
government spending equal to 20% of GDP, roughly the average of post WWII levels. The
weighting parameters on labor and on government spending are chosen such that with the
current level of debt (100%) it would be optimal to spend 20% of GDP on public goods and
to workN = 1_{3} hours.

12

I chose 2011 because I have not been able to get newer data on the amount that matures within the next 10 years so I took the data from Bohn (2011).

### 4

### Long run implications

Before analyzing transitional paths one has to decide how to allocate the free resources as a result of the lower debt to GDP ratio and therefore lower interest expenses. In general, one can either increase public consumption or reduce the tax rate. The approach usually taken in the literature, as for example in Coenen et al. (2008) or Forni et al. (2010), is that all free resources are used for the instrument that was used in the consolidation process. That is if government spending (the tax rate) was reduced (increased) during the transition, then all the proceeds would be used to increase government spending (reduce tax rates) in the long-run. This will have a feedback effect on the household behavior, as for instance lower taxes increase the incentive to work, whereas higher spending has a negative wealth effect. A disadvantage of such an approach is that comparisons between different fiscal measures might be driven the transitional dynamics, but also partly by comparing different steady states. As an alternative, I will determine the optimal composition of tax rates, govern-ment expenditure and private consumption that maximizes the households welfare for a given (lower) debt level. I thus assume that, for reasons outside of the model, the government decides not only to reduce debt levels but also to converge to a new steady state in which this debt level implies an optimal allocation of the other aggregate variables. The remaining task is then to assess which instrument to use in order to transit from the same steady state A to the same steady state B. However, a drawback is that a path for the other instrument that is not used for consolidation has to be chosen, although the results do not depend on specific functional forms of the other instrument. I also checked the approach taken by the literature and the results did not change in an important way, so the long-run behavior seems not to be driving the results in this exercise.

To get the optimal allocation of variables for a given debt amount I thus set up a Lagrangian that maximizes the households welfare function given the constraints 5, 6, 8, 15, 20 and 22. As this is a long-run perspective only equations 8, 15, 20 and 22 bind. One can show that it boils down to the following Lagrangian:

L(N, τ, G;γ1, γ2) =u(N−G)−v(N) +g(G)+ γ1 M C(1−τ)−χnNφ(N−G)σc | {z } labor−leisure +γ2 M Cτ N−G−i4Nd¯new | {z }

gov. budget constraint

Maximization leads to 4 equations and 4 unknowns (N, τ, G, γ2) that can only be solved nu-merically. Table 3 shows the results of private and public consumption, hours worked and the tax rate for debt to GDP ratios of 100% to 90% and 80%. Additionally it shows the

allocation at the first best level of debt. The percentage change is relative to the initial debt level of 100% except for tax rates where the percentage point change is used.

The additional funds from lower debt repayments are used to reduce distortionary tax rates and to increase public good provision. As a result of two effects the households will decide to work more: First, lower tax rates increase the incentive to work by reducing the intra-temporal labor-leisure distortions. Second, the increase in permanent government consumption consti-tutes c.p. a negative wealth effect that induces the agent to work more as in Coenen et al. (2008). While in their analysis private consumption is crowded out in my setting it rises due to the simultaneous lowering of distortionary tax rates. The table also reports the welfare equivalent consumption variation (CV) that is required every period to make the household in the initial steady state as well off as in the new one. More precisely, denote withV(· · ·) life time utility, that is

V (1 +ζ)Cold, Nold, Gold= ∞

X

t=0

βtU (1 +ζ)Cold, Nold, Gold

= 1

1−βU (1 +ζ)C

old_{, N}old_{, G}old

Then

V (1 +ζ)Cold, Nold, Gold≡V(Cnew, Nnew, Gnew) (24)

such that

U (1 +ζ)Cold, Nold, Gold

≡U(Cnew, Nnew, Gnew) (25)

ζ > 0 implies that the household asks for a compensation to be indifferent between both states, that is, they prefer the new state. In the example, households demand 0.18% of permanent consumption such that they do not want to have lower debt levels. With a 20 percentage points reduction it is 0.36% and one can show that the linear relation persists, at least for reasonable consolidation ranges. The qualitative result is robust to different CRRA-parameters in the utility function for private or public consumption and for different mark-ups and Frish elasticities.

### 5

### Transition dynamics

While the previous analysis has shown potential welfare gains from lower debt levels in the long-run, this section sheds some light on potential costs during the consolidation period and whether an equilibrium with lower debt levels is preferable relative to the status quo if the transitional adjustment is taken into account. I will first present each consolidation separately, compare them and then show the importance of a maturity-structure above one period.

Priv. cons. Hours Public good Tax rate CV 100% debt to GDP 0.2667 0.3333 0.0667 0.2885 (starting point) 90% debt to GDP 0.2674 0.3344 0.6700 0.2842 0.271% 0.330% 0.565% -0.428pp 0.1801% 80% debt to GDP 0.2681 0.3355 0.0674 0.2799 0.540% 0.652% 1.101% -0.858pp 0.3577% First best 0.3431 0.4369 0.0938 -0.200 -943% debt to GDP 28.677% 31.068% 40.6321% -48.885pp 8.250% Table 3: Steady state comparison for different debt levels. CV is the welfare equivalent consumption variation.

5.1 Fiscal consolidation

Figure 2 shows the aggregate effects for a tax-based consolidation. The fall in the debt target induces the labor tax rate to rise until period 6 and then to gradually convert back to its new (lower) value τnew. As a result of higher distortionary labor taxes the incentive to supply labor is reduced which causes a recession. Additionally government spending will be higher in the new long run equilibrium. Therefore, the increase in government spending constitutes a negative wealth effect and lowers private consumption while increasing the supply of labor. This effect lowers the output drop, for instance compared to Coenen et al. (2008), to about 2%. The recession is quite pronounced and lasts for 5 to 6 years until labor supply recovers and converges to its higher long-term equilibrium. As taxes reduce c.p. the after-tax wage income, households ask for higher pre-tax wages to compensate part of the income loss. Since wages are marginal costs for firms they react to that by charging a higher prices which leads to inflation. The monetary authority follows the Taylor principle and raises its policy rate more than one-to-one, driving up the real short-term interest rates.

As can be seen from equation (4), the interest expenses of the portfolio il_{t} is a weighted
average of interest rate on previously issued bonds il,n_{t} which themselves depend on the
ex-pected future path of the policy rate it if one iterates (6) forward. Since the model is solved

incorporating perfect foresight, agents take into account the complete path of future policy
rates, that is the initial increase and the gradual fall. Therefore, the interest rate on newly
issued long-term debt il,n_{t} increases but less pronounced than the policy rate. Additionally,
the average interest rate is a weighted sum of its previous value il_{t}−1 and the new financing
cost il,n_{t} and thus reacts only sluggishly by a mere 0.4% compared to 2.5% of the policy rate.
Finally, the increased debt paymentsil,n_{t} bl,n_{t} do not affect the budget a lot as only a relatively
small fraction compared to the outstanding stock is reissued. As one can see at the upper

10 20 30 40 50 60 92 94 96 98 100 Quarters Debt to GDP in %

Actual debt ratio
Debt target
10 20 30 40 50 60
0
0.5
1
1.5
2
2.5
3
**Tax rate**
%−points deviation
Quarters 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
**Inflation**
%−points deviation
Quarters
10 20 30 40 50 60
−2
−1.5
−1
−0.5
0
**Output**
% deviation from ss
Quarters 10 20 30 40 50 60
0
0.1
0.2
0.3
0.4
0.5
**Government spending**
%−points deviation
Quarters 10 20 30 40 50 60
0
0.5
1
1.5
2
2.5
Quarters
%−points deviation

**Nominal interest rate**

i

i_{L}

Figure 2: Tax-based consolidation. Notes: All variables are in percentage deviation from steady state, except tax rates, inflation and interest rates which are in percentage point deviations.

right panel of figure 2, the inflation rate is higher in magnitude than the rise in the nominal
financing costs iL_{t}. Therefore, financing costs in real terms are reduced.13 Summing up, the
rise in the inflation rate lowers the real value of debt, while financing costs increase
moder-ately which reduces the necessary fiscal adjustment. This will be important (and taken up
again) when compared to a one-period debt model.

Figure 3 depicts the same variables for the spending-based scenario. Focusing on the big
picture first, public good provision will be reduced up to 18% in period 6 and recovers
grad-ually until it reaches its higher long run level Gnew. For the households, lower government
spending is a positive wealth effect which leads them to increase private consumption but
also cut working hours which drives the economy into a recession. As a result of lower public
demand firms decrease their prices to attract private demand which drives down the inflation
rate. Monetary policy responds by cutting the short-term interest rate, but, similar to the
argument made above, the reduction in the long-term nominal interest rateiL,n_{t} is muted since
first, the complete future path of all policy rates is taken into account and second, only part
of the debt is reissued while for the other part interest rates are predetermined at the higher

13

After a while inflation is below the average long-term rate thus increasing financing costs of the outstanding debt stock. However, as the total stock is reduced that effect is of smaller importance, especially since the magnitudes are much smaller.

10 20 30 40 50 60 90 92 94 96 98 100 Quarters Debt to GDP in %

Actual debt ratio
Debt target
10 20 30 40 50 60
−18
−16
−14
−12
−10
−8
−6
−4
−2
0
**Government spending**
% deviation from ss
Quarters 10 20 30 40 50 60
−1
−0.5
0
0.5
1
**Inflation**
%−points deviation
Quarters
10 20 30 40 50 60
−1.5
−1
−0.5
0
0.5
**Output**
% deviation from ss
Quarters
10 20 30 40 50 60
−0.4
−0.35
−0.3
−0.25
−0.2
−0.15
−0.1
−0.05
0
**Output**
%−points deviation
Quarters
10 20 30 40 50 60
−1.5
−1
−0.5
0
0.5
1
1.5
Quarters
%−points deviation

**Nominal interest rate**

i

i_{L}

Figure 3: Spending-based consolidation. Notes: All variables are in percentage deviation from steady state, except tax rates, inflation and interest rates which are in percentage point deviations.

steady state level. Additionally, deflation raises the real amount of debt such that total debt financing becomes more expensive and thus the adjustment process more severe. That is the reason why spending has to be cut by such a large amount.

The figure also shows an initial jump of inflation, output and the policy rate. The reason is an anticipation effect: With perfect foresight the households know the exact path of government spending and foresee that it will be much lower during the transition which constitutes a positive wealth effect and implies a growing private demand. However, in the first periods, spending is not yet reduced as much, so to increase private consumption there has to be more output and thus agents need to supply more work.14 That explains the jump in output and, due to more demand, the increase in the inflation rate. If the reaction coefficient on the devi-ation of debt from its targetφgis increased in magnitude, one can show that there is always a

recession and deflation, so that initial spike depends on the specification used. Nevertheless, that first increase in the inflation rate reduces the financing costs of the debt-portfolio in the beginning, but once inflation starts to fall, financing costs are increased. Compared to Coenen et al. (2008), spending reductions are associated with relatively milder recessions. The reason is that in that consolidation period the tax rate is reduced simultaneously which increases the

14

A stronger case can be made if the government announces a credible reduction of spending in the future. This would still increase private demand today and lead to an expansion in output.

2 3 4 0 0.05 0.1 0.15 0.2 0.25 0.3 Year

Output loss relative to debt reduction

**Fiscal Sacrifice Ratio**

Tax hike Spending cut

Figure 4: Fiscal Sacrifice RatioξT, calculated as in (26).

incentive to work and thus cushions the drop in GDP. The importance of future composition of variables on current dynamics is shown, for instance, by Cogan et al. (2013).

5.2 Comparing both fiscal consolidations

Both consolidation strategies lead to the same long run equilibrium, but also entail adjustment costs associated with the transition. Spending-cuts reduce welfare enhancing public purchases while tax-hikes lead to a cut in private consumption. While one can assess the aggregate dynamics from figures 2 and 3, it is instructive to aggregate these effects into one number that is easily comparable. I use two metrics to compare the relative desirability/associated costs.

The first is the “Fiscal Sacrifice Ratio” (FSR), a measure, that relates the output loss to the percentage point reduction of debt. For a smoother comparison I use the average output drop rather the exact drop within that period. More precisely, the ratio is defined as

ξT = 1 T PT t=1 Yt−Yold Yold dT −dold (26) Figure 4 presents the ratio at a two, three and four year horizon. Within two years, both fiscal consolidations reduce the debt to GDP ratio by about 3.5% points while output falls on average about 1%, consistent with a FSR of around 1/3. Increasing the time horizon reduces the sacrifice ratio as growth will catch up to its new long run level.15 Over the whole time span tax-based consolidation is associated with a slightly lower FSR than a spending-based

15_{In the first year, both sacrifice ratios are negative, however, spending cuts are preferable as output growth}

reduces the debt ratio while tax-hikes lead to a recession with an initial increase in debt. A quantitative comparison is thus difficult.

CV Spending-based Tax-based

ζ -0.06 +0.04

Table 4: Welfare equivalent consumption variation ζ, calculated as in (27).

one. A second approach is to evaluate the welfare equivalent consumption variation (CV) associated with each reduction scenario, that is the permanent amount of consumption that makes the household indifferent between staying at the steady state with higher debt and moving to a lower debt world, taking into account the transitional dynamics. It is defined as

V (1 +ζ)Cold, Nold, Gold≡

∞ X t=0 βtU Ct, Nt, Gt (27)

where againV(· · ·) denotes life time utility at the old steady state. ζ >0 implies that agents ask for permanent consumption in order to be indifferent between staying with higher debt levels and moving towards a world with lower debt. In such cases consolidation is actually welfare enhancing. On the other side, ifζ <0 it is better to have a less negative ζ since then overall welfare losses are lower. The corresponding CVs are given in table 5. Thus, similar to the FSR, tax-based adjustments are preferable relative to spending-based ones since its CV is higher. On top, the results also imply that households actually want to consolidate when it is done by raising taxes since their life time utility is higher in that case. With spending-cuts, the transitional costs are too high such that it would be welfare detrimental. As the next subsection shows, these results depend crucially on the average maturity.

5.3 Importance of the average maturity of debt

How much of the results above are driven by the introduction of long-term debt and the implied channels?16 To shed more light on this issue I conduct two experiments: First, I evaluate the aggregate responses for both fiscal adjustments when only short-term debt is available and second, focus on the FSR and the CV for intermediate values of maturity. The nice feature of the model is that it nests the one-period debt case whenγ = 1. Figures 5 and 6 depict the dynamics of the same variables above where everything else is kept constant except γ. Qualitatively, the aggregate responses are similar for both cases. The increase in the tax rate raises inflation and the financing costs of the government and lowers GPD. Sim-ilarly, spending reductions lower the inflation rate, the financing costs and depress output. However, at least for the tax-based scenario, the quantitative results differ markedly:

16

As a reminder there are two main channels: First, financing costs of the portfolio do not change a lot since newly issued debt responds on the whole expected path of policy rates, not only the initial response and just part of the debt is reissued under new financing conditions, for the rest it is predetermined. Second, inflation reduces the real amount of debt more, the higher its average maturity.

10 20 30 40 50 60
92
94
96
98
100
Quarters
%−points deviation
**Debt to GDP**

Actual debt ratio Debt target 10 20 30 40 50 60 0 1 2 3 4 5 Quarters

%−points deviation from ss

**Tax rate**

Long term debt Short term debt

10 20 30 40 50 60 −1 −0.5 0 0.5 1 1.5 2 2.5 Quarters

%−points deviation from ss

**Inflation**

Long term debt Short term debt

10 20 30 40 50 60
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
0
Quarters
% deviation from ss
**Output**

Long term debt Short term debt

10 20 30 40 50 60
0
0.1
0.2
0.3
0.4
0.5
Quarters
% deviation from ss
**Government spending**

Long term debt Short term debt

10 20 30 40 50 60 −1 0 1 2 3 Quarters

%−points deviation from ss

**Long term interest rate**

Long term debt Short term debt

Figure 5: Tax-based consolidation with short-term debt. Notes: All variables are in percent-age deviation from steady state, except tax rates, inflation and interest rates which are in percentage point deviations. The lower right panel displays the variableiL

t which coincides

The labor tax rate roughly doubles to 5% points which leads to an output drop of more than 3% that is also more persistent. In the first periods inflation is actually reduced since the expected loss in income outweighs the increase in the marginal costs. It is only after that initial period that the inflation rate is positive, but nevertheless, in the beginning, financing costs are reduced due to the Taylor-principle. Afterwards inflation starts to rise as high as 2.5%, but that does not reduce the real value of debt since interest rates are adjusted more than one for one and that higher rate is applied to the whole debt stock, driving up total financing costs as illustrated by the lower right panel of figure 5. This explains why taxes have to rise relatively more compared to the long-term debt benchmark. As a result of the deeper recession and less inflationary impact the debt to GDP ratio drops by more and thus raises the tax rate.

In the spending-based adjustments, public goods still have to be cut by roughly 18% but recover much more quickly. One can see at the upper panel on the right in figure 6 that the slightly stronger reduction is enough to push the economy into a deflation over the whole consolidation period. This lowers the financing costs of the government since the central bank cuts its policy rate, but in the initial period deflation actually increases the real amount of debt and thus the necessary adjustment is more pronounced. After that impact is gone, the low financing costs allow the government to quickly increase its spending back to its new level. Output follows that pattern quite closely. Overall, the aggregate variables do not move that much compared to the tax-based consolidation.

Figure 7 illustrates the different sacrifice ratios for the model with short-term debt. Now, spending-cuts become much more preferable than tax-hikes. That result was anticipated due to the much stronger decline in economic activity when taxes are raised. Across the consoli-dation period (2 to 4 years) the FSR is between 3 to 5 times lower when public expenditures are adjusted. The CV confirms that taxes are much more disruptive as its value is negative and much lower than for spending-cuts which implies higher welfare costs of the transitions. The case of one-period debt illustrates that the average maturity of debt affects the macroe-conomic implications of tax- versus spending-based consolidations and changes the relative preferred option. This implies a turning-point from which on tax-hikes are associated with lower disruptions due to the channels mentioned above. To find that maturity-threshold I simulate the model for a couple of different average maturities ranging from one-period debt to as long as 14 years. Here I only plot the two measures to compare both adjustments in figure 8: Since the FSR is an average measure for a given horizon, I chose the 2-year horizon. It is very high for tax-hikes and short maturities but falls relatively quickly. Spending-cuts do not affect the FSR that much since the maturity did also not change the aggregate responses

10 20 30 40 50 60
90
92
94
96
98
100
Quarters
%−points deviation
**Debt to GDP**

Actual debt ratio Debt target 10 20 30 40 50 60 −0.4 −0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 Quarters

%−points deviation from ss

**Tax rate**

Long term debt Short term debt

10 20 30 40 50 60 −1 −0.5 0 0.5 1 Quarters

%−points deviation from ss

**Inflation**

Long term debt Short term debt

10 20 30 40 50 60
−2
−1.5
−1
−0.5
0
0.5
Quarters
% deviation from ss
**Output**

Long term debt Short term debt

10 20 30 40 50 60
−18
−16
−14
−12
−10
−8
−6
−4
−2
0
Quarters
% deviation from ss
**Government spending**

Long term debt Short term debt

10 20 30 40 50 60 −2 −1.5 −1 −0.5 0 Quarters

%−points deviation from ss

**Long term interest rate**

Long term debt Short term debt

Figure 6: Spending-based consolidation with short-term debt. Notes: All variables are in
percentage deviation from steady state, except tax rates, inflation and interest rates which
are in percentage point deviations. The lower right panel displays the variable iL_{t} which
coincides with the policy rate in the case of short-term debt.

CV Spending-based Tax-based

ζ -0.01 -0.13

Table 5: Welfare equivalent consumption variation with short-term debt, calculated as in (27).

a lot in the one-period debt model. The CV marks a more continuous picture: It is mono-tonically increasing (decreasing) when consolidation is tax-(spending-)based the higher the average maturity. The threshold after which tax-based consolidation is preferable is about 2 years for the CV or 4 years for the FSR. Additionally, for maturities above 3 years house-holds are actually better off with a tax-based debt consolidation, but spending-based ones are welfare enhancing relative to the status quo.

### 6

### Remarks

Before I conclude in the final section I want to give some remarks about robustness, possible extensions and limitations.

2 3 4 0 0.5 1 1.5 2 2.5 Year

Output loss relative to debt reduction

**Fiscal Sacrifice Ratio**

Tax hike Spending cut

Figure 7: Sacrifice ratio evaluated at different times for the model with short-term debt.

2 4 6 8 10 12 14 0.5 1 1.5 2 2.5

Average maturity of debt in years

Ratio

**Fiscal Sacrifice Ratio for different maturities**

Tax hike Spending cut 2 4 6 8 10 12 14 −0.12 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06

Average maturity of debt in years

in %

**Consumption variation for different maturities**

Tax hike Spending cut

Figure 8: Fiscal Sacrifice Ratio and CV evaluated at different maturities for tax- and spending-based consolidation

The main message of this thesis is that the maturity structure of government debt is important to determine the aggregate effects of a fiscal consolidation. I have done some robustness checks with respect to parameter values, the timing and the amount of debt to be reduced. Broadly speaking the main result did not change although quantitatively some changes strengthens and other weakens the mechanisms relative to the benchmark calibration. As an example, the Frish elasticity determines the reaction of hours worked on wage changes. If it is lower, that is hours do not react so much on wage-changes, tax-based consolidation is not so inflationary and thus the distance between the two CV measures narrows. However, if it is higher, the gap actually widens.

Next to these particular choices of parameters is the question of which extensions could alter the results. Since monetary policy is constrained in the US since 2009 a ZLB would be a natural extension. Even though it is not yet implemented, the results should be strength-ened: Spending reductions than increase the real interest rate which dampens private demand, driving the economy into a stronger recession with a further fall in the price level and so on. Tax-hikes will reduce the real rate and thus increase consumption which should dampen the recession and raise inflation.

In Europe, where the monetary union reacts on area-wide inflation the results will proba-bly depend on the size of the economy in the union and its openness. Consider the case for tax-hikes: On the one hand they are inflationary and thus the monetary authority will increase the policy rate which drives up financing costs. The smaller a country the less the policy rate will increase. On the other hand higher prices reduces the real exchange rate and lowers competitiveness which dampens output and increases the necessary adjustments, thus a closed economy seems to cushion these effects. For spending-cuts it should be the other way round: Policy rate cuts are beneficial so it would be preferable to be a big economy, while the competitiveness channel is most pronounced in an open economy.

It is straightforward to extend that model to a situation in which after the consolidation starts only short-term debt is issued. That will reduce part of the financing channel as the newly issued debt will pay higher interest rate.

A question remains how much of the results are driven by these simple rules relative to some optimal criteria. Even though in many applications they can approximate Ramsey policy if they react to the right variables, it is not clear in this setup.

To keep the model as simple as possible I approximated the average maturity in the data by having just one bond with the exact average maturity which seems to be a reasonably well characterization for the US. However, the shape of CV (concave and convex) implies that the composition of maturities is quite important: Suppose, for example, a model with 50%

short-term and 50% 19 quarter debt such that the average maturity is 10Q. With 10Q the model implies a CV of -0.04 for spending-cuts and roughly 0 for tax-hikes. However, the respective number for 50%*one-period debt+50%*19Q debt would imply for tax-hikes a lower and for spending-cuts a larger number, thus closing the distance between both consolidations. A final remark on (possible) policy advice. It is important to note that the mechanism high-lighted in this thesis is only one next to a couple of other trade-offs a policymaker faces. For example there are a couple of yet not much explored distributional consequences (tax-ing capitalists or old generation, tax(tax-ing only rich people or all), questions of international competitiveness or current economic conditions (slack in the economy, high unemployment, monetary policy stance) or uncertainty surrounding those adjustments. On could, however, use this model for instance to argue particularly for a higher tax on oil as this will increase inflation through a higher gasoline price and additionally increases the costs for firms that use oil in the production process.

### 7

### Conclusion

In this thesis I assess the macroeconomic implications of tax-based versus spending-based consolidation through the lens of a New Keynesian model with long-term debt. As it turns out, the introduction of a richer maturity is of first order importance to analyze the relative desirability of the two fiscal measures. With short-term debt spending-cuts are clearly pre-ferred according to the welfare equivalent consumption variation and the fiscal sacrifice ratio. However, if the maturity is long enough, tax-hikes become the preferred option. The reason rests on two steps: First, raising taxes are inflationary through an increase in the marginal costs for firms and lowering spending deflationary through reduced public demand. Second, inflation changes the real amount of debt more, the higher its maturity. Therefore, if the maturity is high enough, tax-hikes become less disruptive as part of the increased inflation reduces the real amount of debt and thus the necessary adjustments. For a quantitative ex-ercise I find that maturity threshold to be around 3 years.

The present analyses clarifies the important role of inflation in the consolidation process, even though raising its target rate directly might either not be desirable because of commitment inconsistencies as in Barro and Gordon (1983) or not feasible as in the case of a small country within a currency union. However, since fiscal changes also effect the inflation rate it is im-portant to keep that mechanism in mind when assessing the relative attractiveness of various debt reduction tools.

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### A

### Overview model equations

A.1 Households λt=Ct−σ (28) Wt(1−τt) =χnNtφCtσ (29) 1 =βEt λt+1 λt 1 +it 1 +πt (30) 1 =βEt λt+1 λt 1 +it 1 +πt 1 +iL,n_{t}−µt+1(1−γ)(iL,nt+1−i L,n t ) (31) bL

_{t}= (1−γ) 1 +πt bL

_{t}−1+bL,nt (32) iL

_{t}bL

_{t}= (1−γ) 1 +πt iL

_{t}−1bLt−1+iL,nt b L,n t (33) A.2 Firms Wt=M Ct(1−α)AtNt−α (34) g

_{t}1 =λtM CtYt+βθEt 1 +πt+1 1 +π g

_{t}1

_{+1}(35) g2

_{t}=λtYt+βθEt 1 +πt+1 1 +π −1 g

_{t}2

_{+1}(36) p∗ = −1 g1 g2 (37) 1 =θ 1 +πt 1 +π −1 + (1−θ) p∗1− (38) ∆ =θ∆t−1 1 +πt 1 +π 1−α + (1−θ) p∗− 1−α

_{(39)}

A.3 Government
bL,n_{t} +τtWtNt=Gt+
γ+iL_{t}_{−1}
1 +π b
L
t−1 (40)

Fiscal rules, either:

τt−τnew=φτ
BL_{t}
4Ynew −d
new
(41)
Gt= (1−ρg)Gnew+ρgGt−1 (42)
or
Gt−Gnew=φg
B_{t}L
4Ynew −d
new
(43)
τt= (1−ρτ)τnew+ρττt−1 (44)

A.4 Monetary Policy

1 +it= (1 +i) 1 +πt 1 +π φπ Yt Ynew φy (45)

A.5 Exogenous rules

At= (At−1)ρaeε
a
t _{(46)}
¯
dt= (1−ρd) ¯dnew+ρbd¯t−1 (47)
A.6 Aggregation
Yt∆1−α =AtNt1−α (48)
Yt=Ct+Gt (49)