Debt and the Eﬀects of Fiscal Policy

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Debt and the Effects of Fiscal Policy

Carlo Favero and Francesco Giavazzi

February 14, 2008

AbstractEquilibrium structural models offiscal policy are solved by impos-

ing the government intertemporal budget constraint and are simulatedunder the equilibrium assumption that the real value of the debt inthe hands of the public must equal the expected present value of gov-ernment surpluses. Empirical models offiscal policy typically do notimpose this condition and usually do not even include debt. This isparticularly surprising in the case of countries where the data revealthat fiscal variables respond to the level of the debt. In this paperwe conduct VAR analysis of US fiscal policy by explicitly includingdebt and the stock-flow identity linking debt and deficits. We applyour methodology to different identification approaches: the structuralVAR approach and the narrative approach. Our main findings are thatthe absence of an effect offiscal shocks on long-term interest ratesafrequent and puzzling result in research based on VARs that omit adebt levelcan be explained by their mis-specification, especially oversamples in which the debt to GDP ratio is very high by its historicalstandards. The explicit inclusion of the debt-deficit dynamics does notalter sizeably the effect offiscal policy on output in standard struc-tural VARs, more sizeable differences are obtained when the narrativeapproach is considered.

Keywords: fiscal policy, public debt, government budget con-straint, VAR models

JEL Classification: H60, E62

We thank Olivier Blanchard, Eric Leeper and Roberto Perotti for useful comments.Francesco Giavazzi thanks the Federal Reserve Bank of Boston for its hospitality whilethis paper was completed.

Favero: IGIER (Universita Bocconi) and CEPR. Giavazzi, IGIER (Universit Boc-coni), MIT, CEPR and NBER.

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1 Introduction

Empirical, VAR based, evidence on the effects offiscal policy is designed toserve the purpose of selecting the appropriate structural model to conductpolicy analysis. As recently pointed out by Chung and Leeper (2007) thereis a potentially very relevant discrepancy between fiscal Dynamic StochasticGeneral Equilibrium models and empirical fiscal VARs.

Equilibrium structural models are solved by imposing the governmentintertemporal budget constraint and are simulated under the equilibriumassumption that the real value of the debt in the hands of the public mustequal the expected present value of government surpluses.

Empirical models of fiscal policy typically do not impose this conditionand usually do not even include debt. This is particularly surprising in thecase of countries where the data reveal a positive correlation between thegovernment surplus-to-GDP ratio and the government debt-to-GDP ratioand thus indicate that fiscal variables respond to the level of the debt. Bohn(1998) finds such a correlation in a century of U.S. data.

In this paper we conduct VAR analysis of US fiscal policy by explicitlyincluding debt and the stock-flow identity linking debt and deficits. We showhow impulse response analysis can be conducted in a fiscal VAR augmentedby the stock-flow relation linking debt and deficit. We treat the debt-deficitrelation as an identity that involves non-linear relationships between the

variables normally included in a fiscal VAR but no additional parameters tobe estimated and no additional shocks to be identified. As a consequence ofthese facts, the computation of impulse responses to fiscal shocks that takesexplicitly on account the government budget constraint is accomplished withsome simple modifications of the standard VAR approach.

As the point we make is independent of the particular assumption adoptedto identify fiscal shocksa thorny issue in the fiscal VAR literature, we applyour methodology to different identification approaches: the structural VARapproach (such as in Blanchard and Perotti, 2002 or in Mountford and Uhlig,2002) and the narrative approach, as in Ramey (2006) or in Romer and Romer

(2007).Our main findings are that the absence of an effect of fiscal shocks on

long-term interest ratesa frequent and puzzling result in research based onVARs that omit a debt levelcan be explained by their mis-specification,especially over samples in which the debt to GDP ratio is very high by itshistorical standards. The explicit inclusion of the debt-deficit dynamics does

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not alter sizeably the effect offiscal policy on output in standard structural

VARs, more sizeable differences are obtained when the narrative approach isconsidered.

The plan of the paper is as follows. In Section 2 we explain why estimat-ing the effects offiscal policy shocks omitting the the level of the public debtis problematic and how VAR analysis with the government budget constraintcan be conducted. Section 3 describes our data. In Sections 4 and 5 we evalu-ate the empirical relevance of our point computing impulse responses to fiscalshocks in models in which the variables are allowed to respond to the levelof the debtwhose evolution over time is determined by the intertemporalgovernment budget constraint. In specifying the response offiscal variables

to the level of the debt we follow Bohn (1998). We then compare these im-pulse responses with those obtained from models that omit the debt level.In Section 4 we use the identification technique proposed by Blanchard andPerotti (2002),; in Section 5 we use the tax shocks identified by Romer andRomer (2007).

The methodology described in this paper to analyze the impact offiscalshocks by taking into account the stock-flow relationship between debt andfiscal variables could be applied to other dynamic models which include sim-ilar identities. One example are the recent discussions (see e.g. Christianoet al, 2005 and Chari et al. 2005) on the importance of including capital as

a slow-moving variable to capture the relation between productivity shocksand hours worked.

2 Fiscal policy VARs and the stock-flow con-

straint

The study of the dynamic response of macroeconomic variables to shifts infiscal policy is typically carried out estimating a vector autoregression of theform

Yt = C0 +kX

i=1

CiYti + ut (1)

where Y includes government spending, taxes, output and other macro-economic variables such as interest rates, consumption and inflation.

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This specification does not consider the stock-flow relation between debt

and deficit and the level the level of the debt-to-GDP-ratio is usually omittedfrom (1). This assumption is potentially very relevant in determining themeasured empirical effects offiscal policy for a number reasons :

a feedback from the level of debt ratio to taxes and government spend-ing could be important in the fiscal reaction functions iffiscal authori-ties attach some weights to debt stabilization. Bohn(1998) shows thatsuch a feedback is statistically significant and economically important:in his study a century of U.S. data reveal a positive correlation be-tween the government surplus-to-GDP ratio and the government debt-to-GDP ratio;

interest rates, a central variable in the transmission of fiscal shocks,depend on future expected monetary policy and on the risk premium:both may be affected by the debt dynamicsfor instance if a growingstock of debt raises fears of future monetization or, in an extreme case,of debt default. The impact of a given fiscal shock on interest rates willbe very different depending on whether the shock produces a path ofdebt that is stable or tends to become explosive1.

effects of the level of debt on inflation and output fluctuations cannotbe ruled out a priori, think of the debate on the validity of the Ricardianequivalence (Barro (1974), Kormendi (1983)) or of the literature on theinflationary effects of the debt See Canzoneri et al.(2001).

It seems therefore important to allow for the fact that taxes, governmentspending, output, inflation and the rate of interestin other words the vari-ables entering Yare linked by an identity, the equation that determineshow the debt ratio evolves over time. These observations naturally lead toreplacing (1) with

Yt = C0 +k

Xi=1

CiYti + i

dt1 + ut (2)

1 Giavazzi, Jappelli and Pagano (2000) find that an increase in taxes can raise privateconsumption if it moves the economy from an unsustainable fiscal path to a sustainable one.Romer and Romer (2007) also find that the effect of a U.S. tax shock on output dependson whether the change in taxes is motivated by the governments desire to stabilize thedebt, or is unrelated to the stance offiscal policy

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where Y0

t = gt tt yt pt it . dt1 is the debt-to-GDP ratio at thebeginning of the period, it is the nominal rate of interest (the average cost ofdebt financing),yt is real GDP growth (the differences of the log of GDP),pt is inflation (the differences of the log of the price level), tt and gt are,respectively, (the logs of) government revenues and government expenditurenet of interest.

Once the debt has been brought into the emprical specification, it becomesimmediately clear that (2) omits an identity that links, dynamically and non-linearly, all variables included in the VAR. This identity is the governmentbudget constraint:

dt =1 + it

(1 +pt) (1 +yt)dt1 +

exp(gt) exp(tt)

exp(yt) (3)

The omission of this relation from the empirical VAR does not allowto consider the endogeneity status of dt, and leads to compute impulse re-sponse functions with respect ot the shock of interest under the untenableassumption of a given level of the debt to GDP ratio. Interestingly (3) doesnot contain any parameter to be identified and estimated or any structuralshock. The special nature of this relation poses an interesting (and solvable)problem for the computation of impulse responses that describe the effect offiscal shocks.

Our objective is to compute the response of gt

tt

ytp

tit

dt

to fiscal shocks. To this end we specify the following model:

Yt = C0 +kX

i=1

CiYti + idt1 + ut (4)

dt =1 + it

(1 +pt) (1 +yt)dt1 +

exp(gt) exp(tt)

exp(yt)Aut = Bet

whereut are the VAR innovations and

et are the structural shocks ofinterest. (4) differs from traditional fiscal VARs in two aspects. First, all

variables in the VAR are allowed to respond to the level of the debt. Thisis simply a multivariate extension of the univariate specification of the fiscalreaction function in Bohn (1988). Second, we endogeneize the debt, and wedo so via an intertemporal relation which does not contain an error, since our

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VAR contains all the variables that are relevant to determine the debt-deficit

dynamics.Note that the identification of structural shocks is unaffected by the in-

clusion of d in the model. Since we treat the debt-deficit relationship as anidentity, the number of shocks remains the same, so that the identificationassumptions used in traditional fiscal VAR are immediately applicable. Also,since there are no parameters to be estimated in the debt-dynamics equation,(4) can be estimated excluding the stock-flow identity.

After all the parameters of interest have been identified and estimated,impulse responses comparable to those obtained from the traditional mov-ing average representation of a VAR can be constructed going through the

following steps:

generate a baseline simulation for all variables by solving (4) dynam-ically forward (this requires setting to zero all shocks for a number ofperiods equal to the horizon up to which impulse responses are needed),

generate an alternative simulation for all variables by setting to onejust for the first period of the simulationthe structural shock of in-terest, and then solve dynamically forward the model up to the samehorizon used in the baseline simulation,

compute impulse responses to the structural shocks as the differencebetween the simulated values in the two steps above. (Note that thesesteps, if applied to a standard VAR, would produce standard impulseresponses. In our case they produce impulse responses that allow forboth the feedback from dti toYt and for the endogeneity ofdt modelledvia (3),

compute confidence intervals via bootstrap methods.2

Two comments are in order before moving to the data.

2 Bootstrapping requires saving the residuals from the estimated VAR and then iteratingthe following steps: a) re-sample from the saved residuals and generate a set of observationfor Yt and dt, b) estimate the VAR and identify strucutral shocks, c) compute impulseresponses going thorough the steps described in the text, d) go back to step 1. By goingthorugh 1,000 iterations we produce bootstrapped distributions for impulse responses andcompute confidence intervals.

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1) What are the sources of potential misspecification of traditional VARs

if the data are generated by (4)? In traditional fiscal VARY already containsall the variables that enter the government intertemporal budget constraintbut it is unlikely that the short lags of g, t, p, y and i that enter (lin-early) traditional fiscal VARs trace the evolution of the debt ratio accuratelyenough. In fact the stock-flow relation implies that dt is the result of a longand non-linear lag dynamics

dt =KXi=0

exp(gti) exp(tti)

exp(yti)

i KYi=o

1 + iti

(1 +pti) (1 +yti)

+

+KYi=o

1 + iti

(1 +pti) (1 +yti)

dtK1

2) What about present value conditions? Chung and Leeper (2007) haverecently shown that that the present value condition that the real value ofthe debt must equal the expected present-value of surpluses generates a setof cross-equation restrictions on traditional fiscals VARs. By augmentingtraditional fiscals VARs with the debt deficit dynamics we follow a differentroute. In fact our impulse responses satisfy by construction period-by-period

the debt-deficit stock-flow relationship. We can therefore evaluate the valid-ity of the tranversality condition by considering the long-run response of dtto fiscal shocks that we derive explicitly and by checking if it converges tozero.

In the next sections we illustrate the empirical relevance of our pointon U.S. data by considering two different ways of identifying fiscal shocks,that are representatives of alternative paths researchers have followed: thetechnique proposed by Blanchard and Perotti (2002) and the "exogenous"tax shocks identified by Romer and Romer (2007) with a narrative approach.

3 The data

We use quarterly data for the U.S. economy since 1960:1, the sample analyzedin Blanchard and Perotti (2002) and extended to 2005:4 in Perotti (2007).Our approach requires that the debt-dynamics equation in (??) tracks the

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path of dt accurately: we thus need to define the variables in this equation

with some care.The source for the different components of the budget deficit and for all

macroeconomic variables are the NIPA accounts (available on the Bureau ofEconomic Analysis website, downloaded on December 7th 2006). yt is (thelog of) real GDP per capita, pt is the log difference of the GDP defla-tor. Data for the stock of U.S. public debt and for population are from theFRED database (available on the Federal Reserve of St.Louis website,alsodownloaded on December 7th 2006). Our measure for gt is (the log of)real per capita primary government expenditure: nominal expenditure is ob-tained subtracting from total Federal Government Current Expenditure (line

39, NIPA Table 3.2 ) net interest payments at annual rates (obtained as thedifference between line 28 and line 13 on the same table). Real per capitaexpenditure is then obtained by dividing the nominal variable by populationtimes the GDP chain deflator. Our measure for tt is (the log of) real percapita government receipts at annual rates (the nominal variable is reportedon line 36 of the same NIPA Table).

The average cost servicing the debt, it, is obtained by dividing net interestpayments by the federal government debt held by the public (FYGFDPUNin the Fred database) at time t 1. The federal government debt heldby the public is smaller than the gross federal debt, which is the broadest

definition of the U.S. public debt. However, not all gross debt representspast borrowing in the credit markets since a portion of the gross federaldebt is held by trust fundsprimarily the Social Security Trust Fund, butalso other funds: the Trust Fund for Unemployment Insurance, the HighwayTrust Fund, the pension fund of federal employees, etc.. The assets held bythese funds consist of non-marketable debt.3 We thus exclude it from ourdefinition of federal public debt.

Figure 1 reports, starting in 1970:1 (the first quarter for which the debtdata are available in FRED), this measure of the debt held by the public asa fraction of GDP (this is the dotted line). We have checked the accuracy of

the debt dynamics equation in (??) simulating it forward from 1970:1 (thisis the continuous line in Figure 1). The simulated series is virtually super-imposed to the actual one: the small differences are due to the presence ofsiegnorage (that we ignore and it is clearly very little relevant empirically), to

3 Cashell (2006) notes that "this debt exists only as a book-keeping entry, and does notreflect past borrowing in credit markets."

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approximation errors in computing inflation and growth rates as logarithmic

differences, and to the fact that the simulated series are obtained by usingseasonally adjusted measures of expenditures and revenues. Based on thisevidence we have used the debt dynamics equation to extend dt back to1950:1. (A quarterly series for dt extending back to 1950:1 will becomenecessary when we compare our results with those in Romer and Romer(2007) whose sample starts just after World War II.) Figure 1 shows thatthis series tracks the annual debt level accurately, at least up to the early1950s. 4

4 Fiscal shocks identifi

ed from SVARsWe start by estimating on our data a traditional fiscal Structural VAR(SVAR) as in Blanchard and Perotti (2002) and extended in Perotti (2007)(B&P in what follows).

We consider the following VAR:

Yt = C0 +kX

i=1

CiYti + ut (5)

Y

0

t =

gt tt yt pt it

Aut = Bet

Following B&P and optimal lag-length choice criteria the length of thelag polynomilal in the VAR is set to four quarters. We apply B&P method-ology also to impose restrictions that allow the two structural fiscal shocksin (5) to be recovered from the reduced form residuals, u. The innovationsin the reduced form equations for taxes and government spending, ugt and u

tt,

contain three terms: (i) the response of taxes and government spending tofluctuations in macroeconomic variables, such as output and inflation, that

is implied by the presence of automatic stabilizers; (ii) the discretionary re-sponse offiscal policy to news in macro variables and (iii) truly exogenousshifts in taxes and spending, the shocks we wish to identify. B&P exploit the

4 We are unable to build the debt series back to 1947:1, the start of the Romer andRomer sample, because data for total governemnt spending, needed to buld the debtseries, are available on a consistent basis only from 1950:1.

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fact that it typically takes longer than a quarter for discretionary fiscal policy

to respond to news in macroeconomic variables: at quarterly frequency thecontemporaneous discretionary response of fiscal policy to macroeconomicdata can thus be assumed to be zero. To identify the component of ugt andutt which corresponds to automatic stabilizers they use institutional informa-tion on the elasticities of tax revenues and government spending to macro-economic variables. They thus identify the structural shocks to g and t byimposing on the A and B matrices in Au = Be the following structure 5:

1 0 agy agp agi0 1 aty atp ati

a31 a32 1 0 0a41 a42 a43 1 0a51 a52 a53 a54 1

ugt

uttuyt

uptt

uit

=

b11 0 0 0 0b21 b22 0 0 0

0 0 b33 0 00 0 0 b44 00 0 0 0 b55

egtette1te2te3t

where eit (i = 1, 2, 3) are non-fiscal shocks and have no structural inter-pretation. Since agy , agp, agi, aty, atp and ati are identified using externalinformation 6, there are only 15 parameters to be estimated. As there arealso 15 different elements in the variance-covariance matrix of the 5-equationVAR innovations, the model is just identified. The eit (i = 1, 2, 3) are de-rived by imposing a recursive scheme on the bottom three rows of A and

B; however, the identification of the two fiscal shocksthe only ones that weshall use to compute impulse responsesis independent of this assumption.Finally, the identification assumption imposes b12 = 0.

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5 Mountford and Uhlig (2002) identify government spending and revenue shocks byimposing restrictions on the sign of impulse responses. Fatas and Mihov (2001) rely on aCholeski ordering.

6 The elasticities of taxes and government spending with respect to output, inflationand interest rates used in the identification have been updated in Perotti (2007) and are

Elasticities of government revenues and expendituresagy agp agi aty atp ati

Entire sample 0 -0.5 0 1.85 1.25 01960:1-1979:4 0 -0.5 0 1.75 1.09 01980:1-2006:2 0 -0.5 0 1.97 1.40 0

7 B&P provide robustness checks for this assumption by setting b21 = 0 and estimatingb12. We have also experimented with this alternative option. In practice, as the top leftcorner of the Bmatrix is not statistically different from a diagonal matrix, the assumptionb12 = 0 is irrelevant to determine the shape of impulse response functions.

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Although we use the same identifying assumptions, our choice of variables

differs slightly from those used in B&P, because, as discussed above, weneed to use variables that allow the debt dynamics equation to track thepath of dt accurately. In particular, our measure of i is the average cost ofdebt financing rather than the yield to maturity on long-term governmentbonds used in B&P. Our definitions of g and t are also slightly different: wefollow the NIPA definitions by considering net transfers as part of governmentexpenditure, rather than subtracting them from taxes.

To check that our slight differences in data definitions do not change theresults we have first estimated (1) as in B&P. Following Perotti (2007) whofinds differences in the impulse response functions before and after 1980, the

sample is split in two sub-samples 1960:1-1979:4 and 1980:1-2006:2. Theimpulse responses are reported in Figures 2.1 and 2.2 are consistent withthose reported in B&P. In particular:

an (exogenous) increase in public expenditure has an expansionary ef-fect on output, while an (exogenous) increase in revenues is contrac-tionary. The impact offiscal policy weakens in the second sub-sample,in particular the effects of tax shocks become insignificant;

after 1980 fiscal shocks become less persistent;

the effect offiscal shocks on interest rates is insignificant in the first sub-sample; it is small, significant but counterintuitive in the second sub-sample when an increase in public spending lowers the cost of servicingthe debt;

fiscal shocks have consistently no significant effect on inflation.

These results, however, should be interpreted with some caution.

Figure 3 reports the responses of the debt/GDP ratio to fiscal shocks,obtained just adding to (1) the intertemporal budget constraint. The figure

shows that temporary shocks to expenditure and revenue have a permanenteffect of the debt/GDP ratio, implying, in these cases, an unstable debtdynamics. This feature is particularly prominent in the second subsample,where, as shown by Figure 4, the U.S. economy moved from a situation whereGDP growth exceeded to cost offinancing the debt to a situation where theconverse has been true.

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A permanent effect of temporary fiscal shocks on the debt ratio is a very

unwelcome feature for the empirical model. First, because impulse responseswill be computed along debt paths that are very unlikely. Second, becausethese impulse responses cannot be used to evaluate DSGE models, sincethese models (as pointed out by Chung and Leeper, 2007) typically includethe government budget constraint and are simulated under the equilibriumassumption that the real value of debt in the hands of the public must equalthe expected present-value of surpluses. It is obviously impossible to comparethe empirical evidence from a model that delivers an explosive path for thedebt, with the paths of variables generated by forward looking models, sincesuch models do not have a solution when the debt dynamics is unstable.

4.1 Estimating the effects of fiscal shocks in a SVARwith debt dynamics

We now consider the structural VAR that includes a debt feedback ansd thegovernment intertemporal budget constraint

Yt =kX

i=1

CiYti + i (dt1 d) +A1Bet (6)

dt =

1 + it

(1 +pt) (1 +yt)dt

1 +

exp(gt) exp(tt)

exp(yt)

The specification of (6) is suggested by the empirical findings in Bohn(1998), who estimates a fiscal reaction function in which d is the the un-conditional mean of the debt ratio over a U.S. sample running 1916 to 1995(d = .35). We also identify d as the sample average of the debt ratio (whichhappens to be equal to .35 also in our chosen sample).We model the targetlevel of the debt as a constant on the basis of the evidence of stationarity ofd, pointed out by Bohn(1988) and confirmed in our sample. Given that allrelations in the VAR contain a constant, our results are robust to alternative

choices of d

. The lag-length of (6) is kept to four quarters as in (1)Table 1 reports the estimated coefficients on (dt1 d) in the five equa-

tions (taxes, spending, output, inflation and the cost of debt service) in thetwo sub-samples.

[INSERT TABLE 1 HERE]

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The estimated coefficients show a significant stabilizing effect of the debt

level on the primary surplus. In the first sub-sample (1960:1-1979:4) thisstabilizing effect works through the response of taxes to deviations of thedebt from the target level; in the second sub-sample (1980:1- 2006:2) it worksthrough the response of expenditures. The cost of financing the debt alsoresponds to (dt1 d

): interestingly, such response is significant only in thefirst sub-sample when the level of the debt is further away from its samplemean, our proxy for d.

The finding that the coefficients on (dt1 d) are significant suggests

that the correct VAR to be used in analyses of fiscal policy is one in whichfiscal variables respond to the level of the debt, or its deviation from a target

level. In other words, the VARs normally used to study the effects offiscalpolicy shocks omit a slow moving variable. We shall assess the empiricalrelevance of this omission by comparing the impulse responses of a traditionalVAR with those generated by (6).

The effects of fiscal shocks in a model with feedbacks

Figures 5.1 and 5.2 compare the impulse responses obtained from (6)(reported with a dotted line) with those obtained in a SVAR without a debtfeedback (reported with a continuous line). In both cases we use the sameidentifying assumptions. Figure 5.1 refers to the first sub-sample, 1960:1-

1979:4; Figure 5.2 to the later period. In eachfi

gure the left-hand panelsrefer to a one percent shock to g; the right-hand side panels refer to anequivalent shock to t. In each column the graphs show, from top to bottom,the impulse response ofg, t, y, inflation, and the average cost of debt service.The reported confidence bounds are for the impulse responses with a debtfeedback.

Pre-1980:

following a positive shock to g, allowing for a debt feedback resultsin a larger response of interest rates and inflation (outside the 95%

confidence bounds). For interest rates the divergence widens over time,as debt accumulates,

following a positive shock to t, interest rates fall more in the modelwith feedback and the difference (between the two impulse responses)widens over time,

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the output effect of a shock to g is larger in the model with a debt

feedback.

Post-1980:

The effect ofg shocks on output is dampened in a model with feedback;t shocks have no significant effect on output,

g and t shocks are less persistent in the model with feedback as thestabilization motive acts to dampen the effect of the initial shock,

the response of interest rates to a positive g shock is still negative atthe beginning, but rises over time in the presence of a feedback

Figure 6 compares the responses of the debt level to fiscal shocks ina traditional fiscal VAR and in a model with feedback. Including thefeedback eliminates the possibility that a temporary fiscal shock mightpermanently affect d..

Table 2 complements the result in Figures 5.1 and 5.2 by computing thecumulative response of interest rates and output to a fiscal shock over threehorizons, (4, 12 and 20 quarters) and comparing them with the responses in

the absence of a debt feedback.

In the first sub-sample the effect of a 1% g shock on interest rates, cu-mulated over 20 quarter is 0.10 in the model with feedback, 0.04 without.This difference however disappears after 1980. This result suggests that theresponse of interest rates to the debt level is stronger the further the debtis from its sample mean, our proxy for d. The expansionary effect of an in-crease in expenditure is less pronounced in the model with feedback in bothsubsamples, as the reaction ofg to the level of the debt counteracts the initialshock.

[INSERT TABLE 2 HERE]

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5 Fiscal shocks identified from the narrative

record

Romer and Romer (2007) (R&R in what follows) use the U.S. narrativerecordpresidential speeches, executive-branch documents, and Congressionalreportsto classify the size (defined as the estimated revenue effect of a newtax bill), timing, and principal motivation for all major postwar tax policyactions.8 They then identify, among all documented tax actions, those thatcould be classified as "exogenous", as opposed to those that were counter-cyclical, i.e. motivated by a desire to return output growth to normal. Ex-ogenous tax changes are further divided into two groups: those that appear

to be motivated by a desire to raise the potential growth rate of the econ-omy, and those aimed at reducing a budget deficit inherited from previousadministrations.

Since 1947 U.S. Federal laws changed taxes in 82 quarters. A numberof these quarters had tax changes of multiple types. Among the 104 sepa-rate quarterly tax changes identified, 65 are classified as exogenous. In thisSection we use these 65 tax changes (the R&R exogenous tax shocks) andask what difference it makes if the debt channel is, or is not, included in thetransmission mechanism.

R&R estimate the impact of tax shocks on output using a single-equation

approach:

yt = 0 +12Xi=1

iText1

Yt1+

kXj=1

jZtj + et (7)

where yt is real quarterly output growth,Tex

t1

Yt1are the tax shocks,

measured as a percent of nominal GDP, and Ztj are controls (lags ofyt,monetary policy shocks, government spending, oil prices). The Z0s are as-sumed to be exogenous, and in particular unaffected by the tax shocks, noteven with a lag. The R&R exercise should thus be interpreted as asking the

following (hypothetical) question: Assume that the transmission mechanism8 Early attempts at applying to fiscal policy the methodology proposed by Romer and

Romer (1989) to identify monetary policy shocks were Edelberg, Eichenbaum and Fisher(1999), Burnside, Eichenbaum and Fisher (2004), Ramey (2006). These papers used adummy variable which identifies characterizes episodes of significant and exogenous in-creases in government spending (typically wars).

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of tax shocks is shut down and that such shocks only affect output directly,

rather than, for instance, also via their effect on interest rates. What is theireffect on output under this hypothesis? R&R find that "exogenous" tax in-creases have a larger negative effect on output than countercyclical tax hikes.Among the exogenous tax increases, those motivated by the aim to rein in abudget deficit are less contractionary.in fact the negative impact on outputis statistically insignificant.

To estimate the effects of the R&R tax shocks when fiscal policy is allowedto respond to the level of the debt we first need to embed these shocks in amodel that doesnt shut down the transmission mechanism. We do this usingthe R&R shocks in the two VARs analyzed above: (1) and (??).9 Therefore,

we estimate the following two models:

Yt =kX

i=1

CiYti + iText

Tt+ ut (8)

Yt =kX

i=1

CiYti +kX

i=1

idti + iText

Tt+ ut (9)

dt =1 + it

(1 +pt) (1 +yt)dt1 +

exp(gt) exp(tt)

exp(yt)

where the variables in Y are, as before, taxes, government spending,output, inflation and interest rates.

Including the R&R tax shocks in a VAR is a natural way of computingthe dynamic response of macro variables to shocks identified outside the VARbecause what matters are the impulse responses generated by the differentshocks, not the correlation of the shocks themselves.10 The R&R shocks arevalid shocks to taxes because we find that they are uncorrelated with all lagsof the variables included in the VARs and are significant only in the equation

9 R&R scale their shocks by the level of GDP. We scale them by taxes to allow direct

comparability of the effects of these shocks with those identified in a SVAR. In a SVAR taxshocks are extracted from a specification in the logarithms of the levels of real variables.Innovations thus have the dimension of a percentage change in taxes. A one per centchange in taxes is much smaller than a one per cent shock in the tax-to-GDP ratio. There-scaling affects the size of the effects but not the shape of the impulse responses.

10 VARs have been used to compute impulse responses to shocks identified outside theVAR in the analysis of the effects of monetary shocks in Bagliano and Favero (1999).

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for t. Thus they satisfy the properties that exogenous shocks identified in a

structural VAR should fulfill.Figure 6 shows the impulse response of output to an exogenous R&R tax

shock equivalent to 1% of taxes. Impulse responses are computed usingthree different models:

(7), the equation estimated by R&R where we have replacedTex

t1

Yt1with

Text1

Tt1,

(8), a VAR that excludes a debt feedback

(9), a model that allows the variables in the VAR to respond to the

level of the debt.

The R&R shocks start in 1947, while our data, for the reasons noted infootnote 2, only start in 1950:1: we thus miss the exogenous shocks thatoccurred between January 1947 and December 1949. As in the previousSection we split the sample in two parts: 1950:1-1979:4 and 1980:1-2006:2.

The effects on output of the exogenous R&R tax shocks are quite differentin the two sub-samples and depending on the model they are embedded in.In the first sub-sample (1950:1-1979:4) the contractionary effect of a tax hikeis larger when Z is endogeneized in a model that includes the level of the debtand the government intertemporal budget constraint. This probably happensbecauseas documented in the previous Section (i) a single-equation partialequilibrium approach cannot take into account the persistent effect on taxa-tion of the initial shock and (ii) the fact that fiscal shocks could cumulateover time amplifying the effect on output of an initial impulse.

In the second sub-sample, when the burden of debt stabilization falls onexpenditure -an exogenous increase in taxes is compensated by a subse-quent expenditure accommodation. This explains why, analyzing the effectsof shocks in a model where Z is endogenous and fiscal policy responds to thedebt level, produces much smaller output effects compared with the R&R sin-gle equation model. Figure 7 shows that in fact, in the second sub-sample,

an initial positive tax shock is accompanied by further tax changes in theopposite direction. Following the initial shock taxes fall: when this happensthe effect on the budget is compensated by increases in spending. These re-sponses are not captured in (7) because the equation sets to zero the dynamicresponse of all variables, with the only exception of output growth, to taxshocks.

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6 Conclusions

Motivated by the empirical findings in Bohn (1998), we have analyzed theeffects of fiscal shocks allowing for a direct response of taxes, governmentspending and the cost of debt service to the level of the public debt (as a ratioto GDP). We have shown that omitting such a feedback can result in incorrectestimates of the dynamic effects offiscal shocks. We suggested in particularthat the absence of an effect of fiscal shocks on long-term interest ratesafrequent finding in research based on VARs that omit a debt feedback and donot endogeneize debt dynamicscan be explained by their mis-specification,especially over samples in which the debt to GDP ratio is very high by itshistorical standards.

The methodology described in this paper to analyze the impact offiscalshocks by taking into account the stock-flow relationship between debt andfiscal variables could be extended to other dynamic models which includesimilar identities. For instance, the recent discussions on the importance ofincluding capital as a slow-moving variable to capture the relation betweenproductivity shocks and hours worked (see e.g. Christiano et al, 2005 andChari et al. 2005) could benefit from an estimation technique that tracksthe dynamics of the capital stock generated by the relevant shocks. Thesame applies to open economy models that study, for instance, the effectsof a productivity shock on the current account (see e.g. Corsetti et al.,2006) and that typically omit a feedback from the stock of external debt onmacroeconomic variables.

This approach could also be used in the analysis of the effects of fiscalshocks on debt sustainability, an issue which cannot be addressed in thecontext of a VAR that fails to keep track of the debt dynamics. Stochasticsimulations of(??) could also be used to evaluate the sustainability of currentsystematic fiscal policy and to compute the risk of an unstable debt dynamicsimplied by the current policy regime.

7 References

Bagliano, Fabio and C. Favero [1999]: "Information from financial mar-kets and VAR measures of monetary policy", The European EconomicReview, 43, 825-837.

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Barro R.J. [1974] "Are Government Bonds Net Wealth?" Journal of Political

Economy , 82, 6, 1095-1117

Blanchard, Olivier and R. Perotti [2002]: "An Empirical Characterizationof the Dynamic Effects of Changes in Government Spending and Taxeson Output", Quarterly Journal of Economics

Bohn, Henning [1998]: The Behaviour of U.S. public debt and deficits,Quarterly Journal of Economics, 113, 949-963.

Burnside, Craig, M. Eichenbaum and J.D.M. Fisher [2003]: Fiscal Shocksand Their Consequences, NBER Working Paper No 9772

Canzoneri M.,R. Cumby and B.Diba [2001] "Is the Price Level Determinedby the Needs of Fiscal Solvency, American Economic Review, Vol. 91,No. 5, 2001, pg.1221 - 1238.

Cashell, Brian W. [2006]: "The Federal Government Debt: its size andeconomic significance" CRS Report for Congress.

Chari V.V., P.J. Kehoe and E.R. McGrattan [2005]: "A Critique of Struc-tural VARs Using Business Cycle Theory", Federal Reserve Bank ofMinneapolis Research Department StaffReport 364

Christiano, Lawrence J., M.Eichenbaum and R.Vigfusson [2005]: "AssessingStructural VARs", mimeo

Chung Hess and D.Leeper [2007]: "What has Financed Government Debt?"NBER WP 13425

Corsetti, Giancarlo, L. Dedola and S. Leduc [2006]: "Productivity, ExternalBalance and Exchange Rates: Evidence on the Transmission Mecha-nism Among G7 Countries, forthcoming

Edelberg, Wendy, M. Eichenbaum and J. D.M. Fisher [1999]: Understand-ing the Effects of a Shock to Government Purchases, Review of Eco-nomics Dynamics, pp.166-206, 41

Fats, Antonio and I. Mihov [2001]: The Effects of Fiscal Policy on Con-sumption and Employment: Theory and Evidence, mimeo, INSEAD

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Giavazzi, Francesco, T. Jappelli and M. Pagano [2000]: "Searching for Non-

Linear Effects of Fiscal Policy: Evidence from Industrial and Develop-ing Countries", European Economic Review, 44, no. 7, June.

Kormendi, Roger C. [1983] Government Debt, Government Spending, andPrivate Sector Behavior. American Economic Review 73 , 994-1010.

Mountford, Andrew and H. Uhlig [2002]: What Are the Effcets of FiscalPolicy Shocks? CEPR Discussion Paper 3338

Perotti, Roberto [2007]: In Search of the Transmission Mechanism of Fiscalpolicy"; NBER Macroeconomic Annual, forthcoming

Ramey, Valerie [2006]: "Identifying Government Spending Shocks: Its Allin the Timing", mimeo, July

Romer, Christina and David H. Romer [1989]: Does Monetary Policy Mat-ter? A new test in the spirit of Friedman and Schwartz in Blanchard,O. and S. Fischer, (eds.), NBER Macroeconomics Annual, Cambridge,MIT Press, 4, 121-170

Romer, Christina and David H. Romer [2007]: The Macroeconomic Effects

of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks",mimeo, March.

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0.0

0 .2

0 .4

0 .6

0 .8

1 .0

55 6 0 65 70 7 5 80 85 90 95 00 05

D Y D Y_I

Figure 1: Actual (DY) and simulated (DY_I) (dynamically backward andforward starting in 1970:1) debt-GDP ratio. Actual data are observed at

quarterly frequency from 1970 onwards and at annual frequency from 1970backward. The simulated data are constructed using the government

intertemporal budget constraint (2) with observed data and initialconditions given by the debt-to-GDP ratio in 1970:1.

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- . 0 0 2

. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

. 0 0 8

. 0 1 0

. 0 1 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 6

- . 0 0 5

- . 0 0 4

- . 0 0 3

- . 0 0 2

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 4

- . 0 0 2

. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

. 0 0 8

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 8

- . 0 0 4

. 0 0 0

. 0 0 4

. 0 0 8

. 0 1 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

. 0 0 4

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0- . 0 0 5

- . 0 0 4

- . 0 0 3

- . 0 0 2

- . 0 0 1

. 0 0 0

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 6

- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

. 0 0 0 2

. 0 0 0 4

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

. 0 0 0 2

. 0 0 0 4

. 0 0 0 6

. 0 0 0 8

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 4

- . 0 0 0 3

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

. 0 0 0 1

. 0 0 0 2

. 0 0 0 3

. 0 0 0 4

. 0 0 0 5

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 5

- . 0 0 0 4

- . 0 0 0 3

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

. 0 0 0 1

. 0 0 0 2

. 0 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

s hoc k s t o l _gg s hoc k s to l _ t t

Figure 2.1: Fiscal shocks identified from a SVAR:1960:1-1979:4. The firstcolumn shows responses to shocks to gt; the second column to shocks to

tt.The responses reported along the rows refer, respectively, to the effectson gt, tt, yt, pt, it.

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. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

. 0 0 8

. 0 1 0

. 0 1 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 7

- . 0 0 6

- . 0 0 5

- . 0 0 4

- . 0 0 3

- . 0 0 2

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 4

- . 0 0 3

- . 0 0 2

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

. 0 0 4

. 0 0 5

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 4

. 0 0 0

. 0 0 4

. 0 0 8

. 0 1 2

. 0 1 6

. 0 2 0

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

. 0 0 4

. 0 0 5

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 2

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 5

- . 0 0 0 4

- . 0 0 0 3

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

. 0 0 0 1

. 0 0 0 2

. 0 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 4

- . 0 0 0 3

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

. 0 0 0 1

. 0 0 0 2

. 0 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 9

- . 0 0 0 8

- . 0 0 0 7

- . 0 0 0 6

- . 0 0 0 5

- . 0 0 0 4

- . 0 0 0 3

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

. 0 0 0 1

. 0 0 0 2

. 0 0 0 3

. 0 0 0 4

. 0 0 0 5

. 0 0 0 6

. 0 0 0 7

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

s h o c k s t o l_ g g s h o c k s t o l_ t t

Figure 2.2: Fiscal shocks identified from a SVAR:1980:1-2006:3. The firstcolumn shows responses to shocks to gt; the second column to shocks to

tt.The responses reported along the rows refer, respectively, to the effectson gt, tt, yt, pt, it.

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-.0008

-.0004

.0000

.0004

.0008

.0012

.0016

2 4 6 8 10 1 2 14 16 1 8 20

-.0008

-.0004

.0000

.0004

.0008

.0012

.0016

2 4 6 8 10 1 2 14 16 1 8 20

-.003

-.002

-.001

.000

.001

.002

.003

2 4 6 8 10 1 2 14 16 1 8 20

-.009

-.008

-.007

-.006

-.005

-.004

-.003

-.002

-.001

.000

2 4 6 8 10 1 2 14 16 1 8 20

1960-1979

1980-2006

sh ocks to l_gg shocks to l_tt

Figure 3: Response of the debt to GDP ratio to fiscal shocks identified froma SVAR.

- .0 5

. 0 0

. 0 5

. 1 0

. 1 5

. 2 0

. 2 5

6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 0 0 0 5

a v e ra g e c o s t o f fi n a n c in g th e d e b t ( a n n u a li z e d )q u a rte r ly n o m i n a l G D P g ro w th (a n n u a l iz e d )

Figure 4: Average cost of debt financing and quarterly (annualized)nominal GDP growth

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- . 0 0 4

- . 0 0 2

. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

. 0 0 8

. 0 1 0

. 0 1 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0- . 0 0 6

- . 0 0 5

- . 0 0 4

- . 0 0 3

- . 0 0 2

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 6

- . 0 0 4

- . 0 0 2

. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

. 0 0 8

. 0 1 0

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 8

- . 0 0 4

. 0 0 0

. 0 0 4

. 0 0 8

. 0 1 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 2

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

. 0 0 4

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 5

- . 0 0 4

- . 0 0 3

- . 0 0 2

- . 0 0 1

. 0 0 0

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 6

- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

. 0 0 0 2

. 0 0 0 4

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 6

- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

. 0 0 0 2

. 0 0 0 4

. 0 0 0 6

. 0 0 0 8

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

. 0 0 0 2

. 0 0 0 4

. 0 0 0 6

. 0 0 0 8

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 8

- . 0 0 0 6

- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

. 0 0 0 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0


Figure 5.1: Fiscal shocks identifi

ed from a SVAR (solid line) and in modelwith feedbacks (dotted line). Sample 1960:1 1979:4. The first column showsresponses to shocks to gt; the second column to shocks to tt.The responses

reported along the rows refer, respectively, to the effects on gt, tt, yt, pt, it.

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. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

. 0 0 8

. 0 1 0

. 0 1 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 6

- . 0 0 4

- . 0 0 2

. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 4

- . 0 0 2

. 0 0 0

. 0 0 2

. 0 0 4

. 0 0 6

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 8

- . 0 0 4

. 0 0 0

. 0 0 4

. 0 0 8

. 0 1 2

. 0 1 6

. 0 2 0

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

. 0 0 4

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0- . 0 0 2

- . 0 0 1

. 0 0 0

. 0 0 1

. 0 0 2

. 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 5

- . 0 0 0 4

- . 0 0 0 3

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

. 0 0 0 1

. 0 0 0 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0- . 0 0 0 3

- . 0 0 0 2

- . 0 0 0 1

. 0 0 0 0

. 0 0 0 1

. 0 0 0 2

. 0 0 0 3

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 1 0

- . 0 0 0 8

- . 0 0 0 6

- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

- . 0 0 0 4

- . 0 0 0 2

. 0 0 0 0

. 0 0 0 2

. 0 0 0 4

. 0 0 0 6

. 0 0 0 8

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0


Figure 5.2: Fiscal shocks identified from a SVAR (solid line) and in modelwith feedbacks (dotted line). Sample 1980:1 2006:3. The first column showsresponses to shocks to gt; the second column to shocks to tt.The responses

reported along the rows refer, respectively, to the effects on gt, tt, yt, pt, it.

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2 4 6 8 10 1 2 14 1 6 18 2 0

- .014

- .012

- .010

- .008

- .006

- .004

- .002

.000

.002

2 4 6 8 10 12 1 4 16 1 8 20

R& R

VAR w i thou t IGBC

V A R w i t h IG B C

195 0:1 -198 0:4 19 81:1 -20 06 : 2

Figure 7: Using the Romer and Romer (2007) tax shocks. Effect on outputin different models

- . 0 1 6

- . 0 1 2

- . 0 0 8

- . 0 0 4

. 0 0 0

. 0 0 4

. 0 0 8

. 0 1 2

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

gt

yD p

id

Figure 8: Dynamic response of all variables to an R&R tax shock, in a VARwith a debt feedback estimated over the sample 1950:1-1980:1.

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Table 1 The effect ofdt1 d in a VAR (st. errors in parenthesis)

gt tt yt pt it

dt

1

d

1960:1-1979:4 0.1970.101

0.2250.650

0.0820.161

0.0270.006

0.00970.029

1980:1-2006:20.052

0.1290.085

0.0540.0196

0.0420.0067

0.00890.0062

0.0082

Table 2: Cumulative responses of y and i to a g and a t shock

Cumulative responses to g and t shocks equal to 1 per cent (annualized). Bootstrappedconfidence intervals are reported below estimates

Hor without debt feedback with debt feedback

60:1-79:4 80:1-06:2 60:1-79:4 80:1-06:2 60:1-79:4 80:1-06:2 60:1-79:4 80:1-06:2

g shock t shock g shock t shock

y t t40.005, 0.13

0.0650.10, 0.22

0.160.28, 0.15

0.220.06, 0.06

0.00080.01, 0.13

0.060.06, 0.18

0.1250.30, 0.18

0.240.06, 0.07

0.007

t120.15, 0.66

0.3900.48, 0.96

0.701.13, 0.61

0.860.12, 0.39

0.1600.12, 0.65

0.380.42, 0.86

0.6171.14, 0.61

0.840.15, 0.40

0.122

t200.06, 0.94

0.500.82,1.72

1.241.83, 0.91

1.3390.40, 0.74

0.220.02, 0.86

0.410.68, 1.46

1.021.84,0.89

1.300.37, 0.69

0.168

it t40.01, 0.01

0.0030.06, .0.03

0.0450.01, 0.013

0.0030.004, 0.026

0.0090.02, 0.001

0.0070.07, .0.04

0.0550.01, 0.001

0.0060.002, 0.03

0.016

t120.05, 0.05

0.0020.17, 0.098

0.1350.06, 0.05

0.0050.003, 0.112

0.0560.005, 0.06

0.0320.17, 0.10

0.1360.08, 0.03

0.0590.02, 0.12

0.0671

t200.02, 0.10

0.040.27, 0.16

0.210.12, 0.03

0.040.0243, 0.177

0.0990.05, 0.16

0.0980.24, 0.14

0.1890.20, 0.09

0.140.03, 0.19

0.108

Debt and the Eﬀects of Fiscal Policy

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