Article history:Received 2 January 2014

Measuring the effects of discretionary fiscal policy is both difficult and controversial, assome explicit or implicit identifying assumptions need to be made to isolate exogenous

interaction of fiscal and non-fiscal variables in a rather arbitrary way. In this paper, werelax those restrictions and identify fiscal policy shocks by exploiting the conditionalheteroscedasticity of the structural disturbances. We use this methodology to evaluate the

nd the nature ofifferent answersssment of theseethodology thatn this area is then of government

revenue varies automatically with income and is, therefore, predictable. A second reason is that changes in public spending

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Journal of Economic Dynamics & Control

Journal of Economic Dynamics & Control 47 (2014) 1231510165-1889/& 2014 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.jedc.2014.08.004

n Corresponding author. Tel.: 1 514 340 7003; fax: 1 514 340 6469.E-mail address: hafedh.bouakez@hec.ca (H. Bouakez).or taxes may reflect countercyclical policy actions to stabilize the economy or the government's desire to maintain thebudget deficit or public debt at a given level.A classic question in macroeconomics is: how does fiscal policy affect economic activity and welfare? Treceived renewed interest in light of the recent financial crisis and the debate about the relevance agovernment intervention to stimulate the economy. To the extent that different theories provide dregarding the macroeconomic effects of fiscal policy, it is important to have an accurate empirical asseeffects. The purpose of this paper is to provide new evidence on this subject using an alternative empirical mavoids potential shortcomings of existing approaches. The main challenge facing the empirical literature idifficulty to isolate exogenous and unanticipated changes in fiscal policy. One reason is that a large fractiohis question has5 August 2014Accepted 5 August 2014Available online 12 August 2014

JEL classification:C32E62H20H50H60

Keywords:Fiscal policyGovernment spendingTaxesPrimary deficitStructural vector auto-regressionIdentification

1. Introductionmacroeconomic effects of fiscal policy shocks in the U.S. before and after 1979. Our resultsshow substantive differences in the economy's response to government spending and taxshocks across the two periods. Importantly, we find that increases in public spending are,in general, more effective than tax cuts in stimulating economic activity. A key contribu-tion of this study is to provide a formal test of the identifying restrictions commonly usedin the literature.

& 2014 Elsevier B.V. All rights reserved.Received in revised form and unanticipated changes in taxes and government spending. Studies based on structuralvector autoregressions typically achieve identification by restricting the contemporaneousMeasuring the effects of fiscal policy

Hafedh Bouakez a,n, Foued Chihi b, Michel Normandin a

a HEC Montral, CIRPE, 3000 Cte-Sainte-Catherine, Montral, QC, Canada, H3T 2A7b Universit du Qubec Trois-Rivires, Trois Rivires, QC, Canada, G9A 5H7

a r t i c l e i n f o a b s t r a c t

The complexity of the process by which fiscal policy is conducted is not fully captured, however, in existing empiricalstudies that use structural vector auto-regressions (SVAR) to assess the effects of unanticipated shocks to governmentspending and taxes.1 The assumptions commonly employed to identify these shocks are to a large extent arbitrary andsometimes overly restrictive, thus calling into question the validity of the ensuing results. For example, most existing studiesidentify government spending shocks by assuming that public spending is predetermined with respect to any othereconomic variable, including taxes (e.g., Fats and Mihov, 2001a; Blanchard and Perotti, 2002; Gal et al., 2007). Also,following the seminal work of Blanchard and Perotti (2002), tax shocks are typically identified by purging the fraction ofgovernment revenue that changes automatically with output and by assuming that the resulting cyclically adjusted taxes donot respond to contemporaneous changes in government spending. In both cases, these exclusion restrictions whichdefine the policy indicator are insufficient to achieve identification, and so additional restrictions must be imposed on thecontemporaneous interaction of the variables included in the SVAR. These additional restrictions affect the transmission offiscal policy shocks.

In this paper, we estimate the effects of fiscal policy shocks on GDP and domestic absorption in the U.S. using a flexible

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151124SVAR that relaxes the identifying assumptions used in previous studies. We instead achieve identification by exploiting theconditional heteroscedasticity of the innovations to the variables included in the SVAR, a methodology initially proposed byKing et al. (1994) and Sentana and Fiorentini (2001). The presence of conditional heteroscedasticity in the macroeconomictime series typically used in empirical work on fiscal policy has been documented by several existing studies.2 Our empiricalapproach avoids imposing a priori assumptions about the implicit indicator of fiscal policy or its transmission mechanism, asit leaves unrestricted the contemporaneous interaction among fiscal instruments and between those instruments and theremaining variables of interest. Importantly, it also allows us to test various identifying restrictions commonly imposed inthe literature, which are otherwise untestable under the usual assumption of conditional homoscedasticity of the shocks.3

To the best of our knowledge, this is the first attempt to identify fiscal policy shocks and their effects through time-varyingconditional variances.4

Underlying our empirical framework is a simple theoretical model that imposes a minimal structure on the system to beestimated, which insures that fiscal shocks and their effects are uniquely identified. The model casts fiscal policy in thecontext of a market for newly issued government bonds. The supply of bonds may or may not shift as a result of changes intaxes or public expenditures, depending on the government's implicit target or, alternatively, fiscal-policy indicator. In turn,variations in taxes and public expenditures reflect both the automatic/systematic response of these variables to changes ineconomic conditions, and exogenous and unpredicted shifts in policy, i.e., fiscal-policy shocks. The market-clearingcondition for bonds and the government budget constraint then impose a cross-equation restriction on the SVARparameters, thus ensuring that the dynamics of fiscal variables are mutually consistent. An additional advantage of ourtheoretical model is that it allows us to give a structural interpretation to the parametric restrictions associated with thedifferent indicators of fiscal policy.

In order to account for a structural break in the data, we estimate our SVAR over the pre- and post-1979 periods. We startby showing that the inclusion of the price of bonds to the list of variables used in estimation enables us to obtain sharpereconometric inference relative to a 3-equation system that only includes output, government spending and taxes. Althoughthese three series exhibit sufficient time-varying conditional heteroscedasticity to allow estimation and identification, the 3-equation system proves to be uninformative about the identifying restrictions commonly used in the literature. In contrast,inference based on the 4-equation system (which includes the price of bonds) allows us to conclude that while thoserestrictions tend to be generally supported by the data in the pre-1979 period, they are strongly rejected in the post-1979period.

Our results indicate that estimates of the structural parameters differ across the two sub-periods. These differences haveimportant implications for the dynamic effects of fiscal policy shocks on output. In particular, we find that an unexpectedincrease in government spending leads to a larger and more persistent rise in output in the post- than in the pre-1979period. The implied impact multiplier (defined as the dollar change in output that results from a dollar increase in theexogenous component of public spending) increases from 0.93 in the former period to 1.34 in the latter. We also documentthat output has become less responsive to tax shocks after 1979 and that tax cuts are, in general, less effective in stimulating

1 A parallel empirical literature uses the narrative approach to identify exogenous and unanticipated changes in U.S. fiscal policy. Ramey and Shapiro(1998) isolate three events that led to large military buildups in the U.S. (the Korean War 1950:3, the Vietnam War 1965:1, and the Carter-Reagan defensebuild-up 1980:1). They identify exogenous changes in government spending with a dummy variable that traces these episodes. Ramey (2011) isolates moreevents that led the press to forecast increases in defense spending and provides estimates of the present value of the forecasted changes. Romer and Romer(2010) use a variety of government documents to identify, quantify and classify significant changes in federal tax legislation from 1947 to 2007.

2 See, for example, Garcia and Perron (1996), Den Haan and Spear (1998), Fountas and Karanasos (2007), Fernandez-Villaverde et al. (2010), andFernandez-Villaverde et al. (2011).

3 Mountford and Uhlig (2009) propose an alternative agnostic procedure whereby fiscal-policy shocks are identified by imposing sign restrictions onthe impulse responses of fiscal variables and by assuming that these shocks are orthogonal to business-cycle and monetary-policy shocks. WhileMountford and Uhlig's approach leaves unrestricted many of the contemporaneous relations between the variables of interest, it still restricts the responseof fiscal variables to fiscal shocks and requires the prior identification of business-cycle and monetary-policy shocks. Moreover, the sign-restrictionapproach does not allow formal testing of the commonly used identifying restrictions.

4 Identification through heteroscedasticity has been recently applied to study the effects of monetary policy shocks. Rigobon and Sack (2004) assumethat there is a shift in the unconditional variance of the monetary policy shock on days of FOMC meetings, while Normandin and Phaneuf (2004) andBouakez and Normandin (2010) allow the conditional variances of policy and non-policy shocks to follow a parametric process.

economic activity than increases in government spending. Finally, comparing these findings with those obtained byimposing the commonly used identifying restrictions reveals that the discrepancies between the unrestricted and restrictedresults tend to be larger in the post-1979 period. For example, the spending multiplier implied by the unrestricted system inthe post-1979 period is roughly 50 percent larger than that implied by recursive identification schemes. This observation isconsistent with the fact that the commonly used identifying restrictions are found to be soundly rejected by the dataafter 1979.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 125A fundamental question that has received considerable attention in recent years concerns the response of privateconsumption to a government spending shock. Standard neoclassical theory predicts that public spending crowds outprivate consumption due to a negative wealth effect, but the empirical literature provides mixed evidence. Generallyspeaking, SVAR-based studies find that consumption rises in response to an increase in government spending (e.g.,Blanchard and Perotti, 2002; Gal et al., 2007), while those based on the narrative approach find the opposite result (e.g.,Edelberg et al., 1999; Burnside et al., 2004; Ramey, 2011). To shed further light on this issue, we estimate an extendedversion of our SVAR that includes consumption. We find clear evidence of a crowding-in effect of public spending on privateconsumption, but only in the post-1979 period. In fact, we find that the effects of fiscal policy shocks on output largelyreflect the adjustment of private consumption.

In order to check the robustness of our empirical methodology to potential misspecifications of the underlying structuralmodel, which does not explicitly impose all the cross-equation restrictions or stability condition that a microfoundedtheoretical model would imply, we estimate our SVAR using artificial data simulated from a simple neoclassical model inwhich the structural shocks have time-varying conditional variances. We find that our conditional heteroscedasticityapproach to identification is largely successful in pinning down fiscal policy shocks and their effects and that it significantlyoutperforms existing identification approaches based on parametric restrictions.

It is often argued that, due to the legislative and implementation lags inherent in fiscal policy, changes in governmentspending and taxes are likely to be anticipated by economic agents several months before they actually take place, aphenomenon commonly referred to as fiscal foresight (see, for example; Leeper et al., 2008). To the extent that agentsbehave in a forward-looking manner, reacting to news about future fiscal policy, the SVAR approach may fail to correctlyidentify fiscal policy shocks and may therefore lead to biased estimates of their effects. Ramey (2011) provides suggestiveevidence that the SVAR-based innovations are in fact anticipated. More specifically, she finds that the government spendingshocks extracted from a standard SVAR estimated using U.S. data and identified as in Blanchard and Perotti (2002) areGranger-caused by the war dates isolated by Ramey and Shapiro (1998). To verify whether this criticism applies to thegovernment spending shocks implied by our SVAR, we subject them to the same test carried out by Ramey. The test providesno evidence that these shocks are Granger-caused by the war dates.5 We also conduct an analogous check for our tax shocksby testing whether they are Granger-caused by the dates identified by Romer and Romer (2010) as marking theannouncements of exogenous changes in U.S. tax policy. We again find no evidence that these dates predict the SVARtax shocks. These results suggest that the fiscal-foresight problem is not sufficiently severe to undermine the ability of theSVAR approach to identify truly unanticipated shocks to fiscal policy, at least in the sample period considered here.6

The rest of the paper is organized as follows. Section 2 presents the SVAR specification and describes the identificationstrategy, the estimation method and the data. Section 3 reports the estimation results, tests the commonly used identifyingrestrictions, and discusses the properties of the identified fiscal policy shocks. Section 4 studies the dynamic effects of fiscalpolicy shocks, and the implications of imposing the commonly used identifying restrictions. Section 5 extends the baselineSVAR to study the effects of fiscal policy shocks on consumption and investment. Section 6 studies the robustness of ourempirical methodology to potential misspecifications. Section 7 concludes.

2. Empirical methodology

2.1. Specification

We start with the following SVAR:

Azt m

i 1Aizt it ; 1

where zt is a vector of macroeconomic variables and t is a vector of mutually uncorrelated structural innovations, whichinclude fiscal shocks. Blanchard and Perotti (2002) assume that the vector zt consists of output, government spending andtaxes. In our specification, we add to this list the price of government bonds for reasons that will become apparent below.

5 The absence of Granger causality cannot be rejected for alternative measures of government spending shocks reported in the narrative-approachliterature.

6 This is likely due to the fact that an important fraction of fiscal policy shocks are in fact unanticipated. Simulation results by Mertens and Ravn (2010)indeed show that if the data are generated both by anticipated and unanticipated fiscal shocks and that the former explain a relatively small share of thevariance of fiscal variables, the SVAR approach can be successful in uncovering the true impulse responses to an unanticipated fiscal shock. These authorsalso estimate the effects of unanticipated government spending shocks in the U.S. using an augmented SVAR procedure that is robust to the presence ofanticipated effects and find very similar results to those obtained from a standard SVAR.

Denote by t the vector of residuals (or statistical innovations) obtained by projecting zt on its own lags. These residualsare linked to the structural innovations through

At t ; 2where A ai;ji;j 1;;4 is the matrix that captures the contemporaneous interaction among the variables included in zt whilethe matrices A ( 1;;m) capture their dynamic interaction. Note that the matrices A and A are assumed to be constantover timean important assumption for our identification strategy.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151126Extracting the structural shocks from the residuals requires knowledge of the matrix A. As is well known, however, underconditional homoscedasticity of the structural shocks, projecting zt on its own lags does not provide sufficient informationto identify all the elements of A. As discussed below, our empirical methodology relaxes the assumption that the shocks areconditionally homoscedastic and this allows to identify fiscal policy shocks and their effects without having to rely on theidentifying restrictions commonly imposed in the literature. When A is left completely unrestricted, however, identificationis achieved only up to an orthogonal rotation of its columns.7 This implies that the structural shocks, t , cannot beinterpreted economically. In order to put a label on each of these shocks, we impose a minimal economic structure onsystem (1).8 More specifically, we consider the following model:

db;t q;ty;t;tdd;t ; 3

p;t g;t;t q;tsb;t ; 4

g;t gy;tgdd;tg;tgg;t ; 5

;t y;tdd;tgg;t;t : 6Eq. (3) is the private sector's demand for newly issued government bonds (Treasury bills), expressed in innovation form.

It states that the demand for bonds, db;t , depends on the price of bonds, q;t , on disposable income, y;t;t , and on a demandshock, d;t , scaled by the parameter d.

9 The parameter , which measures (the absolute value of) the slope of the demandcurve, is assumed to be positive and different from 1, and is a positive parameter. Rather than taking a stand on the processby which the government determines the quantity of newly issued bonds, we simply require that this quantity satisfies the(linearly approximated) government's budget constraint. The latter is given by Eq. (4), which states that the innovation inthe primary deficit, p;t , (i.e., the difference between government spending and taxes) must be equal to the innovation in thevalue of debt, q;tsb;t , where sb;t is the quantity of newly issued bonds. Note that because this constraint is expressed ininnovation form, it does not include the payment for bonds that mature in period t (since those bonds were issued in periodt1).10 Eqs. (5) and (6) describe the procedures followed by the government to determine fiscal spending and taxes. Thedisturbances g;t and ;t are the fiscal shocks that we aim to identify. The former is a shock to government spending and thelatter is a tax shock. The terms g and are scaling parameters. Eq. (5) states that government spending may change inresponse to changes in output or to demand and tax shocks. Eq. (6) has an analogous interpretation for taxes. In theseequations, the parameters g and measure the automatic and systematic responses of, respectively, government spendingand taxes to changes in output. In this respect, g and do not necessarily coincide with the elasticities of fiscal variableswith respect to output estimated by Blanchard and Perotti (2002), which capture only the automatic adjustment ofgovernment spending and taxes. As we explain below, different procedures to set fiscal policy will be characterized bydifferent values of the parameters ; g ; ; g ; ;g and :

Imposing equilibrium in the bonds market and solving for the structural innovations, t , in terms of the residuals, t , yield

a11 a12 a13 a14 d

1d

1d

1d

g g g g 1g

1g g g 1g

1g gg 1g

1g g gg 1g

g g 1g

1 g 1g

g 1 1g

11 g 1g

0BBBBBB@

1CCCCCCA

vy;tvq;tvg;tv;t

0BBBB@

1CCCCA

1;td;tg;t

;t

0BBBB@

1CCCCA 7

where a1j j 1;;4 are unconstrained parameters.The conditional scedastic structure of system (7) is

t A1tA10; 8

7 See Sentana and Fiorentini (2001), Ehrmann et al. (2011), and Ltkepohl (2013).8 In Section 6, we study the robustness of our methodology to potential misspecifications of this structure.9 Admittedly, this equation does not fully capture demand for U.S. bonds originating from the rest of the world. As it stands, Eq. (3) captures foreign

demand only through its effect on the price of bonds. However, other factors that can potentially affect this demand, such as foreign income and theexchange rate, are subsumed in the term d;t . We chose not to account explicitly for these factors and to go with a more parsimonious system in order toremain as close as possible to existing studies and to reduce the computational burden associated with the heteroscedasticity approach to identification.

10 The government budget constraint (4) omits seignorage, given that this source of revenue has historically been negligible in the U.S. during theperiod considered (less than 0.4 percent of GDP on average, according to our calculations).

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 127where t Et1t0t is the (non-diagonal) conditional covariance matrix of the statistical innovations and t Et1t0t isthe (diagonal) conditional covariance matrix of the structural innovations. Without loss of generality, the unconditionalvariances of the structural innovations are normalized to unity (I Et0t. The dynamics of the conditional variances of thestructural innovations are determined by

t I121t10t12t1; 9where the operator denotes the element-by-element matrix multiplication, while 1 and 2 are diagonal matrices ofparameters. Eq. (9) involves intercepts that are consistent with the normalization I Et0t. Also, (9) implies that all thestructural innovations are conditionally homoscedastic if 1 and 2 are null. On the other hand, some structural innovationsdisplay time-varying conditional variances characterized by univariate generalized autoregressive conditional heterosce-dastic [GARCH(1,1)] processes if 1 and 2 which contain the ARCH and GARCH coefficients, respectively are positivesemi-definite and I12 is positive definite. Finally, all the conditional variances follow GARCH(1,1) processes if 1, 2,and I12 are positive definite.

2.2. Identification

Under conditional heteroscedasticity, system (7) can be identified, allowing us to study the effects of fiscal policy shocks.The sufficient (rank) condition for identification states that the conditional variances of the structural innovations arelinearly independent. That is, 0 is the only solution to 0, such that 0 is invertible where stacks by column theconditional volatilities associated with each structural innovation. The necessary (order) condition requires that theconditional variances of (at least) all but one structural innovations are time-varying. In practice, the rank and orderconditions lead to similar conclusions, given that the conditional variances are parameterized by GARCH(1,1) processes (seeSentana and Fiorentini, 2001).

To understand how time-varying conditional volatility helps with identification, first note that the unconditionalvariances of the statistical and structural shocks are related through

A1A10 : 10Assuming the SVAR includes n variables, the estimate of allows to identify nn1=2 of the n2 elements of A, leavingnn1=2 elements to be identified. Note also that (8) implies

tt1 A1tt1A10: 11

This set of equations allows to identify kk1=2 additional parameters of A, where k is the rank of tt1: Hence, iftt1 has a rank of at least n1, identification can be achieved. In our context, a necessary condition for this is that atleast n1 structural innovation are time-varying.

Under conditional homoscedasticity of the structural disturbances (i.e., when 1 and 2 are null), (8) and (10) coincide, sothat (11) becomes non-informative. In this case, nn1=2 arbitrary restrictions need to be imposed on the elements of A inorder to achieve identification.

To gain some economic intuition for identification through conditional heteroscedasticity, consider the followingsimplified version of (7):

y;t y;ty1;t ; 12

;t y;t;t ; 13where y a14=a11 and y 1=a11. This system consists of a downward-sloping output curve (12) and an upward-slopingtax curve (13), and contains 4 unknown parameters: y, , y, and . For illustrative purposes, assume that 1;t has a time-varying conditional volatility governed by the following GARCH(1,1) process:

1;t 112121;t121;t1; 14while ;t has a constant conditional volatility, which we normalize to 1 (;t 1. Fig. 1 displays the time series of 1;t , 1;t , y;tand ;t , simulated for 2500 periods using equations (12)(14) under the following parametrization: y 0:5, 0:5, y 1, 1, 1 0:3, 2 0:6, i;t 1=2i;t zi;t , and zi;t N0;1 where i 1; . Fig. 2 depicts the scatter plot of y;t and ;t : Forcomparison, Figs. 1 and 2 also show the simulated series under the assumption that both shocks are conditionallyhomoscedastic (1 2 0).

Under conditional homoscedasticity, small and large values of 1;t and ;t are as likely to occur and, as a result, therealizations of y;t and ;t form a spherical cloud in the (y;t , ;t plan. Since shifts in the output and tax curves are as likely togenerate the realizations of y;t and ;t , these realizations are not informative about the slope of either of the two curves. Inother words, y and cannot be identified. One possible strategy then is to use the unconditional scedastic structureassociated with (12) and (13) to identify the parameters y, y, and , and to impose a restriction on : This is precisely theapproach taken by Blanchard and Perotti (2002).

Under conditional heteroscedasticity, process (14) produces alternating episodes of high and low volatility for thestructural innovation 1;t : Importantly, the large swings in 1;t observed during high-volatility episodes mainly translate into

epsilon_1

0

6v_y

0

4

5

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151128-4

-2

gamma_112

-4

-3

-2

-1

v_tau

500 1000 1500 2000 2500 500 1000 1500 2000 2500

42

4

1

2

3more pronounced fluctuations of y;t (relative to those associated with low-volatility episodes), without affecting much thebehavior of ;t : As a result, the scatter plot of y;t and ;t exhibits an elliptical shape along the tax curve. By implying thatlarger values of 1;t (compared to those of ;t) are likely to occur in high volatility periods, conditional heteroscedasticityinduces shifts of the output curve and movements along the tax curve, thus allowing to identify the slope of the tax curve, . The remaining parameters, y, y, and , are identified through the unconditional scedastic structure associated with (12)and (13).

We now show how our empirical model nests various sets of parametric restrictions commonly used in the literature toidentify fiscal policy shocks and their effects.11 These restrictions reflect the econometrician's belief about the relevantpolicy indicator and/or transmission mechanism of fiscal shocks.

2.2.1. Restrictions associated with the policy indicatorThe third equation of system (7) shows how the government spending shock is related to the VAR residuals:

g;t a31y;ta32q;ta33g;ta34;t ; 15

0

2

4

6

8

10

500 1000 1500 2000 2500 500 1000 1500 2000 2500-4

-3

-2

-1

0

1

2

3

Fig. 1. Simulated series. Notes: The simulated series are generated from Eqs. (12)(14). The red lines correspond to the heteroscedastic case and the bluelines to the homoscedastic case. For both cases, the parametrization of Eqs. (12) and (13) is y 0:5, 0:5, y 1, 1, i;t 1=2i;t zi;t , and zi;t N0;1 where i 1; . For the heteroscedastic case, the parametrization of Eq. (14) is 1 0:3 and 2 0:6 so that 1;ta1, while ;t 1. For the homoscedastic case,the parametrization is 1 2 0 so that 1;t ;t 1. (For interpretation of the references to color in this figure caption, the reader is referred to the webversion of this article.)

11 Mountford and Uhlig (2009) propose an alternative identification strategy by imposing sign restrictions on the variables' responses. Their system,however, includes more variables than ours so that their identifying restrictions cannot be nested in our framework. We are therefore unable to test thoserestrictions or to reproduce their results using our set of variables.

_ 0.0

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 129v_tau

v

-4 -2 0 2 4-5.0

-2.5

Fig. 2. Scatter plot of y;t and ;t . Notes: The simulated series are generated from Eqs. (12)(14). The red dots correspond to the heteroscedastic case and theblue dots to the homoscedastic case. For both cases, the parametrization of Eqs. (12 and (13) is y 0:5, 0:5, y 1, 1, i;t 1=2i;t zi;t , andzi;t N0;1 where i 1; . For the heteroscedastic case, the parametrization of Eq. (14) is 1 0:3 and 2 0:6 so that 1;ta1, while ;t 1. For thehomoscedastic case, the parametrization is 1 2 0 so that 1;t ;t 1. The black lines are the output and tax curves. The green lines represent thedownward and upward shifts of the output curve induced by the conditional heteroscedasticity. (For interpretation of the references to color in this figurecaption, the reader is referred to the web version of this article.)wh

Tha3jsinassfisconspethe

y

2.55.0ere

a31 ggg

g1g;

a32 1ggg1g

;

a33 1ggg1g

;

a34 1ggg

g1g:

e term on the right-hand side of Eq. (15) defines the fiscal-spending indicator (in innovation form). Since the coefficientsj 1;;4 are functions of freely estimated parameters, this policy indicator is not constrained to be summarized by agle variable (or a particular subset of variables). This contrasts with existing empirical studies, which make a prioriumptions about the relevant policy indicator in order to achieve identification. Most of these studies assume that theal-spending indicator is government spending (Blanchard and Perotti, 2002; Gal et al., 2007). Fats and Mihov (2001b),the other hand, use the primary deficit as a broad indicator of fiscal policy (i.e., without distinction between governmentnding and tax policies). The parametric restrictions under which government spending and the primary deficit measurestance of fiscal spending are the following:

G indicator (government spending): g g g 0: In this case, changes in government spending are completelypredetermined with respect to the current state of the economy and do not reflect any systematic/automatic response ofthe government. It is easy to show that under these restrictions the policy shock is proportional to the innovation togovernment spending (g;t 1gg;t:PD indicator (primary deficit): g , g and g 1: Under this scenario, the government targets the primary deficitwhen setting fiscal spending. Unexpected changes in the primary deficit therefore reflect purely government spendingshocks (g;t 11 gp;t:

Analogously, the fourth equation of system (7) is

;t a41y;ta42q;ta43g;ta44;t ; 16

41 42 43 44 q;t d;t

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151130where x is the elasticity of taxes with respect to output, which is estimated outside the SVAR. The system above can beobtained by setting a12 0 and x in (7), in addition to the restrictions associated with the G indicator. It is worthemphasizing that the recursive and non-recursive schemes given by (17) and (18) yield identical responses to a governmentspending shock since they both assume that ~a1j 0 (j 2;;4).

To identify the effects of a tax shock, Blanchard and Perotti relax the assumption that ~a12 0 and assume instead thattaxes are predetermined with respect to government spending. This yields

~a11 ~a12 ~a12=x 0~a21 ~a22 ~a23 00 x ~a33 ~a33 0~a41 ~a42 ~a43 ~a44

0BBBB@

1CCCCA

vg;tvy;tv;tvq;t

0BBBB@

1CCCCA

g;t

1;t;t

d;t

0BBBB@

1CCCCA: 19~a21 ~a22 ~a23 0~a31 x ~a33 ~a33 0~a ~a ~a ~a

BBBB@CCCCA

vy;tv;tv

BBBB@CCCCA

1;t

;t

BBBB@CCCCA; 18where

a41 gg

1g;

a42 1g1g

;

a43 g11g

;

a44 11g

1g:

Two cases of interest are nested in the rule above. The first defines the relevant indicator of tax policy as cyclicallyadjusted government revenue, as in Blanchard and Perotti (2002). In the second, the tax-policy indicator is the primarydeficit. The corresponding restrictions are:

CAT indicator (cyclically adjusted taxes): 0: In this case, tax shocks are measured with unexpected changes in thefraction of government revenue that does not vary automatically or systematically with output (;t ;ty;t=: PD indicator (primary deficit): g , g and 1: In this case, tax shocks correspond to unexpected changes in theprimary deficit ;t 1g 1p;t

:

2.2.2. Restrictions associated with the transmission mechanismEach of the policy indicators discussed in the previous section implies 3 different restrictions on the elements of A (2 in

the case of the CAT indicator). Therefore, under conditional homoscedasticity, 3 additional restrictions (4 in the case of theCAT indicator) have to be imposed in order to achieve identification. These restrictions in turn determine the way in whichfiscal shocks affect the endogenous variables over time. In the case of a government spending shock, the literature typicallycompletes identification via a Cholesky decomposition of the covariance matrix of the VAR residuals, which yields threeadditional zero restrictions (see, for example, Fats and Mihov, 2001a; Gal et al., 2007). By ordering government spendingfirst among the variables included in the VAR, this scheme implies that the matrix A in (1) is lower triangular, so that system(7) becomes

~a11 0 0 0~a21 ~a22 0 0~a31 ~a32 ~a33 0~a41 ~a42 ~a43 ~a44

0BBBB@

1CCCCA

vg;tvy;tv;tvq;t

0BBBB@

1CCCCA

g;t

1;t

;t

d;t

0BBBB@

1CCCCA: 17

This identification scheme can be obtained as a special case of system (7) by imposing the following restrictions:a12 a14 0, in addition to three restrictions associated with the G indicator. Note that the ordering of the remainingvariables is irrelevant when computing the effects of a government spending shock.

Blanchard and Perotti (2002) propose an alternative, non-recursive, scheme to identify the effects of a governmentspending shock. In the context of our four-variable SVAR, their identification scheme implies

~a11 0 0 00 1

vg;t0 1

g;t0 1

In this specification, the precise value of x imposed by Blanchard and Perotti captures exclusively the automaticadjustment of taxes to output.12 This system can be obtained from (7) by imposing a12 g g 0 and x, in addition tothe two restrictions associated with the CAT indicator. As shown by Caldara and Kamps (2012), in Blanchard and Perotti'sSVAR, the response of output to a tax shock is entirely pinned down by the value of , for a given (unconditional) covariancematrix, . It can be shown that this is no longer the case in our unrestricted system (7). We discuss this point in furtherdetail in Section 4.2.

Under conditional homoscedasticity, none of the identifying restrictions discussed above can be tested; thus, no formalcriterion can be used to choose among competing identification schemes. This is possible, however, under our identificationmethod (which exploits the conditional heteroscedasticity of the shocks) since it leaves unrestricted the elements of A. Weperform this exercise in Section 3.2.

2.3. Estimation method and data

The elements of A;1, and 2 are estimated using the following two-step procedure. We first estimate by ordinary least

vg;t x ~a11 ~a33;t ~a11

g;t ;

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 131v;t xvy;t 1~a33;t :

This representation is similar to that found in Blanchard and Perotti (2002, p. 1333).13 A constant and a trend are also included among the regressors.14 This system is obtained by setting a12 0, 1, 0, and g 0 in (3)(6). These restrictions imply that the supply and demand for bonds are

indistinguishable or, alternatively, that d;t is a linear combination of 1;t , g;t , and ;t .15 We found the results to be robust when we measure the price of bonds using the return on 10-year treasury bonds.16 Since the price of bonds is that of federal bonds it may be more consistent to consider only federal fiscal variables in the empirical analysis. However,

this would prevent us from directly comparing our results to those of earlier studies (e.g., Blanchard and Perotti, 2002). Still, we checked the robustness ofour results to excluding state and local fiscal variables and found our main conclusions to be fairly robust.

17 All the series, except the interest rate, are seasonally adjusted at the source.18 Perotti (2004) and Favero and Giavazzi (2009) also distinguish between the pre- and post-1980 periods when measuring the effects of U.S. fiscal

policy.squares a 4-equation VAR with four lags (m4) that includes output, the price of bonds, government spending and taxes.13In order to highlight the importance of adding the price of government bonds to our information set, we also estimate a3-equation VAR that only includes output, public spending, and taxes. The 3-equation system underlying such a VAR is arestricted version of (7) given by14

a11 a13 a14g g g 1g

1g 1g

gg 1g

g 1g

1g

11g

0BBB@

1CCCA

vy;tvg;tv;t

0B@

1CA

1;t

g;t

;t

0B@

1CA: 20

From each VAR, we extract the implied residuals, t , for t m1;; T : For given values of the elements of the matrices A;1,and 2, it is then possible to construct an estimate of the conditional covariance matrix t recursively, using Eqs. (8) and (9)and the initialization m m0m I. Assuming that the residuals are conditionally normally distributed, the second stepconsists in selecting the elements of the matrices A;1, and 2 that maximize the likelihood of the sample.

We use quarterly U.S. data from 1960:1 to 2007:4. In their main analysis, Blanchard and Perotti (2002) excluded the1950s on the ground that this period was characterized by exceptionally large spending and tax shocks. Since one of ourobjectives is to compare our results to theirs, we restrict our sample to the post-1960 period, and we closely follow theirapproach in constructing the series used in estimation. Output is measured by real GDP. The price of bonds is measured bythe inverse of the gross real return on 3-month treasury bills,15 where the CPI is used to deflate the gross nominal return.Government spending is defined as the sum of federal (defense and non-defense), state and local consumption and grossinvestment expenditures. Taxes are defined as total government receipts less net transfer payments.16 The spending and taxseries are expressed in real terms using the GDP deflator. The data are taken from the National Income and ProductsAccounts (NIPA), except for the 3-month treasury bill rate, which is obtained from the Federal Reserve Bank of Saint-Louis'Fred database.17 Output, government spending and taxes are divided by total population (taken from Fred) and all the seriesare expressed in logarithm.

The transformed series are depicted in Fig. 3. The series of output, government spending and taxes exhibit a clear upwardtrend, but that of the price of bonds appears to have two distinct regimes separated by a break around the end of the 1970s.This observation suggests that it may not be appropriate to estimate (7) over the entire sample period. To determine thecutoff date in a more formal and precise way, we applied Andrews and Ploberger's (1994) structural break test to detectchanges in the trend of the price of bonds. The test suggests that there is a break at 1979:2. We therefore consider the twosub-periods: 1960:11979:2 and 1979:32007:4.18

12 Note that the first and third equations of (19) can be rewritten as

~a12 1

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 1231511323. Estimation results

3.1. Parameter estimates and specification tests

Before discussing the estimates of the structural parameters and their implications, we perform a preliminary analysis todocument the presence of conditional heteroscedasticity in the series used in estimation. We start by applying themultivariate ARCH test proposed by Fiorentini and Sentana (2009) to the statistical residuals obtained from the 3- and 4-equation VARs. This is a Lagrange multiplier (or score) test of serial correlation in the squares of statistical residuals. The testis applied both to the diagonal and off-diagonal elements of the matrices of the ARCH coefficients at a given lag.19 The testresults, presented in Table 1, indicate that we can strongly reject the null hypothesis of absence of cross-correlation in thesquared statistical residuals. This hints to the presence of conditional heteroscedasticity in the statistical innovations, which,given our assumption that A is constant, reflects time-varying conditional variances of the structural shocks.20

Fig. 3. Transformed data.

19 The 2-distributed test statistic involves the sample autocovariances of the squares and cross-products of the estimated statistical innovations, aswell as weighting matrices reflecting the unobservability of these innovations. Intuitively, this Lagrange multiplier test can be interpreted as a test based onthe orthogonality conditions: Et0tt0tk 0, where Et0t and k is a given lag.

20 In principle, time-varying conditional volatility in the reduced-from residuals may also be caused by structural change or other types of non-linearity not captured by our SVAR. For example, if A were time varying (as is assumed by Auerbach and Gorodnichenko, 2012, for example), then theresiduals may have time-varying variances even if the structural shocks are homoscedastic.While the time-varying-parameter approach allows to obtain state-dependent estimates of the effects of fiscal policy shocks (something that our

methodology does not enable us to do), it still requires imposing some parametric restrictions in order to achieve identification, which in itself can be asource of misspecification. Pinning down the deep source of conditional heteroscedasticity in macroeconomic time series is beyond the scope of this paper,but is certainly an interesting avenue for future research.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 133Table 1Multivariate ARCH test for the VAR residuals.

Lag 3-Equation VAR 4-Equation VAR

1960:11979:2 1979:32007:4 1960:11979:2 1979:32007:4A visual inspection of the conditional variances of the structural shocks extracted from system (7), depicted in Fig. 4,reveals that both fiscal and non-fiscal shocks exhibit significant conditional heteroscedasticity in both sub-samples,displaying alternating episodes of high and low volatility. A similar observation holds for the structural shocks extractedfrom the 3-equation system (not reported). This suggests that the order condition for identification (that at least n1 shockshave time-varying conditional variances) is satisfied. This observation corroborates the findings of earlier studies thatdocument the presence of conditional volatility in the time series of output (Fountas and Karanasos, 2007), the interest rate

1 0.000 0.000 0.000 0.0002 0.000 0.000 0.000 0.0004 0.000 0.000 0.000 0.000

Note: Entries are p-values of the 2-distributed Lagrange multiplier test statistic.

Fig. 4. Conditional variances of the shocks.

(Garcia and Perron, 1996; Den Haan and Spear, 1998; Fernandez-Villaverde et al., 2010), and fiscal variables (Fernandez-Villaverde et al., 2011).

Interestingly, on several occasions, the spikes in the conditional volatility of government spending and tax shocks,displayed in Fig. 4, coincide with the public spending and tax shocks identified by Ramey (2011) and Romer and Romer(2010), respectively. For example, the peaks in the conditional volatility of public spending shocks observed in 1967:2,1973:1, 1989:1, and 2001:4 generally concur with the unanticipated increases in U.S. defense spending reported by Ramey

Table 2Multivariate ARCH test for the structural shocks.

Lag 3-Equation system 4-Equation system

1960:11979:2 1979:32007:4 1960:11979:2 1979:32007:4

1 0.000 0.000 0.000 0.0012 0.134 0.000 0.461 0.0004 0.000 0.000 0.000 0.307

Note: Entries are p-values of the 2-distributed Lagrange multiplier test statistic.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151134(2011). Likewise, the spikes in the conditional volatility of tax shocks observed in 1975:1 and 2004:2 coincide with theexogenous tax cuts identified by Romer and Romer (2010).

Table 2 reports the results of the FiorentiniSentana multivariate ARCH test to verify the presence of conditionalheteroscedasticity in the structural shocks. Strictly speaking, this is not a test of the joint significance of the parameters in(9). Such a test cannot be performed because conventional critical values are invalid under the null hypothesis of conditionalhomoscedasticity, given that systems (7) and (20). become underidentified. However,it is possible to apply Fiorentini andSentana's test using an identified version of the SVAR,i.e.,a version in which enough restrictions are imposed on the matrix Ato ensure identification.21 In carrying out this test, we exploit the idea that a GARCH process can be approximated by anARCH process of a sufficiently high order. Since the structural shocks are orthogonal, the test is applied only to the diagonalelements of the matrices of the ARCH coefficients at a given lag. Table 2 shows that, both for the 3- and 4-equation systems,the null hypothesis that the ARCH coefficients are jointly equal to 0 at lags 1, 2, and 4 is generally rejected by the data,implying that the conditional variances of the structural innovations are time-varying.

To determine whether the GARCH(1,1) specification provides an adequate description of the process that governs theconditional variances of the structural innovations, we test whether there is any autocorrelation in the ratio of the squaredstructural innovations relative to their conditional variances. The McLeod-Li test results, reported in Table 3, indicate thatthe null hypothesis of no autocorrelation cannot be rejected (with one exception) at conventional significance level for 1, 2and 4 lags. This suggests that the GARCH(1,1) process is well specified.

Table 4 reports estimates of the structural parameters. With a few exceptions, the estimates differ across the two periods,thus confirming the presence of instability and justifying the need to focus on sub-periods rather than the entire sampleperiod. Generally speaking, we obtain similar estimates for the parameters that are common to the 3- and 4-equationsystems. One exception is , for which the 3-equation system yields a larger estimate in the post- than in the pre-1979period, whereas the 4-equation system implies the opposite result. The estimated values of , however, are consistent withavailable estimates (see Caldara and Kamps, 2012).22

21 An advantage of Fiorentini and Sentana's test is that the numerical value of the test statistic is invariant to the specific identifying restrictionsimposed on A.

22 The only case in which we obtain a relatively small value of is when the four-equation system is estimated using post-1979 data. This low value of , however, should not be viewed as being inconsistent with the U.S. tax system. Indeed, if measured only the automatic response of tax revenue to

output, then, owing to the progressivity of the U.S. tax system, this elasticity should be substantially larger than 1. But our estimate of captures both theautomatic and systematic response of taxes to output. If the systematic component is a concave function of output, this will drive down the overall elasticityof taxes with respect to output.To see this, consider the simple case where the tax rate, tA0;1, is flat and there is no systematic response of taxes to output. In this case, the elasticity of

tax revenue to output will be equal to 1. This elasticity captures the automatic response of taxes to output.Now, assume that there is a component of tax revenues that responds systematically to output. Assume also that this component is an increasing and

concave function of output. More specifically,

T tY|{z}automatic

ln Y|{z}systematic

other factors;

where T is tax revenue, Y is output, and is a positive parameter. In this case, the elasticity of tax revenue with respect to output is

d ln Td ln Y

tYtY ln Yo1 if ln Y41:

A final caveat about the interpretation of is that given that we measure taxes as total government receipts less net transfer payments, is, strictlyspeaking, not a pure automatic/systematic output elasticity of taxes.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 135Table 3Specification test results.

Squared structural innovations Lag 3-Equation system 4-Equation system

1960:11979:2 1979:32007:4 1960:11979:2 1979:32007:4

21;t 1 0.731 0.198 0.579 0.534

2 0.794 0.327 0.099 0.7364 0.867 0.383 0.144 0.358Recall that the model presented in Section 2 imposes restrictions only on the parameters and . The former has to bepositive and different from 1, while the latter must take a positive value. The requirements for are satisfied in both periods,but we obtain a positive estimate of only for the post-1979 period. None of the point estimates is precise, however. Ourmodel also implies that the linear restriction a21a23 a24 must hold. A likelihood-ratio test of this restriction indicatesthat it cannot be rejected at standard significance levels in any of the two sub-periods (see Table 5). This suggests thatsystem (7) represents an adequate specification of the data, so we henceforth refer to it as the unrestricted system and to itsimplications as the unrestricted ones. As stated above, this system can be used to test the identifying restrictions associatedwith the various indicators of fiscal policy and with the different transmission mechanisms usually assumed in theliterature. In this regard, it is important to emphasize that despite the uncertainty surrounding the individual estimates of

2d;t 1 0.972 0.592

2 0.982 0.3544 0.698 0.166

2g;t 1 0.496 0.871 0.544 0.968

2 0.665 0.364 0.713 0.5944 0.763 0.194 0.722 0.313

2;t 1 0.450 0.293 0.852 0.642

2 0.269 0.108 0.781 0.7134 0.217 0.186 0.679 0.219

Note: Entries are the p-values associated with the McLeodLi test statistic applied to the squared structural innovations relative to their conditionalvariances.

Table 4. Estimates of the structural parameters.

Parameter 3-Equation system 4-Equation system

1960:11979:2 1979:32007:4 1960:11979:2 1979:32007:4

15.100 13.906(89.079) (22.075)

0.777 3.802(10.901) (4.765)

g 0.216 0.194 0.224 0:204(0.721) (0.155) (0.249) (0.281)

1.323 1.679 1.913 1.085(0.726) (0.737) (0.973) (0.673)

g 0.001 0.006(0.032) (0.017)

0.026 0.133(0.173) (0.225)

g 0.097 0.018 0.097 0.027(0.111) (0.089) (0.158) (0.088)

0.280 0.407 0.293 0.183(0.666) (1.072) (0.782) (0.676)

d 0.140 0.122(0.871) (0.203)

g 0.010 0.008 0.010 0.008(0.002) (0.001) (0.002) (0.001)

0.036 0.027 0.029 0.024(0.011) (0.002) (0.007) (0.008)

Note: Figures between parentheses are standard errors.

Table 5Test of the restriction: a21a23 a24.

1960:11979:2 1979:32007:4

B. Tests of the restrictions associated with the transmission of fiscal policy

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151136Spending policyCholesky a13 0 0.226 0.653Blanchard and Perotti x 0.162 0.605P-value 0.319 0.104

Note: P-values are those of the 2-distributed likelihood-ratiotest statistic.

Table 6ATests of commonly used identifying restrictions (3-equation system).

Type Restrictions 1960:11979:2 1979:32007:4

A. Tests of alternative indicators of fiscal policySpending policyG g g 0 0.158 0.444PD g , g 1 0.090 0.007

Tax policyCAT 0 0.707 0.504PD g , 1 0.091 0.008structural parameters, we show below that we are often able to reject the joint restrictions associated with the commonlyused identifying assumptions.

3.2. Tests of the commonly used identifying restrictions

As stated above, the parametric restrictions imposed in earlier SVAR-based studies can be divided into two categories:those characterizing the policy indicator and those associated with the transmission of fiscal policy. Both sets of restrictionsare tested using a likelihood-ratio test, and the results are reported, respectively, in Panels A and B of Table 6A in the case ofthe 3-equation system and Table 6B in the case of the 4-equation system.23 We also test the two sets of restrictions jointly,and report the results in Panel C of each table.24

Starting with the 3-equation system, Table 6A shows that the restrictions associated with the most common policyindicators, namely, the G indicator in the case of spending policy and the CAT indicator in the case of tax policy, as well asthe restrictions associated with their transmission mechanism cannot be rejected either individually or jointly in any of thetwo sub-periods. In fact, the only restrictions that can be rejected (at the 5 percent significance level) within the 3-equationsystem are those associated with the PD indicator in the post-1979 period.

In contrast, as shown in Table 6B, the 4-equation system implies that while the restrictions associated with the Gindicator are generally supported by the data, those associated with the transmission of spending policy are stronglyrejected in the post-1979 period. Moreover, when these two sets of restrictions are tested jointly, they are also found to be

Tax policyBlanchard and Perotti g 0 and x 0.579 0.496

C. Joint tests (Indicator Transmission)Spending policyCholesky g g a13 0 0.226 0.653Blanchard and Perotti g g 0 and x 0.162 0.605

Tax policyBlanchard and Perotti g 0 and x 0.579 0.496

Notes: Entries are p-values of the 2-distributed likelihood-ratio test statistics. x is fixed to 1.75 in 1960:11979:2 and 1.97 in 1979:32007:4. For the jointtest, we only report the results involving the restrictions associated with the G indicator for the spending policy and the CAT indicator for the tax policy.

23 Blanchard and Perotti (2002) estimate the average output elasticity of taxes, x, to be 2.08 based on data from 1947:1 to 1997:4. In our tests, however,we consider the values of 1.75 and 1.97 estimated by Perotti (2004) for the periods 1960:11997:4 and 1980:12001:4, respectively.

24 For the joint tests, we only focus on the restrictions involving the G and CAT indicators (that is, we ignore the PD indicator), since these are by far themost widely used indicators in the SVAR literature.

Table 6BTests of commonly used identifying restrictions (4-equation system).

PD g , g , 1 0.063 0.004

B. Tests of the restrictions associated with the transmission of fiscal policySpending policy

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 137rejected by the data after 1979. Regarding the tax policy, the results based on the 4-equation system reveal that therestrictions associated with the CAT indicator are consistent with the data in the 1960:11979:2 period, but are rejectedafter 1979, whereas the restrictions associated with the transmission of tax policy cannot be rejected by the data at the 5percent level in any of the two sub-periods. When the two sets of restrictions are tested jointly, they are found to be rejectedin the post-1979 period.

These results convey three important messages. First, although there is sufficient time variation in the conditionalvolatility of output, taxes and government spending to achieve identification in (and to allow the estimation of) the 3-

Cholesky a12 a14 0 0.155 0.001Blanchard and Perotti a12 0 and x 0.152 0.000

Tax policyBlanchard and Perotti a12 g g 0 and x 0.093 0.149

C. Joint tests (Indicator Transmission)Spending policyCholesky g g g a12 a14 0 0.186 0.011Blanchard and Perotti g g g a12 0 and x 0.085 0.010

Tax policyBlanchard and Perotti a12 g g 0 and x 0.200 0.005

Notes: Entries are p-values of the 2-distributed likelihood-ratio test statistics. x is fixed to 1.75 in 1960:11979:2 and 1.97 in 1979:32007:4. For the jointtest, we only report the results involving the restrictions associated with the G indicator for the spending policy and the CAT indicator for the tax policy.Type Restrictions 1960:11979:2 1979:32007:4

A. Tests of alternative indicators of fiscal policySpending policyG g g g 0 0.293 0.670PD g , g , g 1 0.063 0.004

Tax policyCAT 0 0.571 0.004equation system, this source of information turns out to be insufficient to allow sharp econometric inference, hence theimportance of including the price of government bonds among variables used in estimation. The conditional hetero-scedasticity characterizing this series makes our estimated framework much more informative about the data generatingmodel, thus enabling us to reject counterfactual identifying restrictions.25 Therefore, from now on, we will discard the 3-equation system and focus only on the results based on the 4-equation system.

Second, our test results corroborate the conclusion reached by Blanchard and Perotti (2002) based on institutionalinformation that there is little evidence of a contemporaneous response of government spending to economic activity, aview that has become widely accepted in the literature. This suggests that the commonly used identifying assumption thatinnovations to government spending are exogenous is a plausible one.

Third, purging the automatic/systematic response of tax revenues to output is not sufficient to isolate the purelyexogenous component of tax changes, at least when focusing on the post-1979 period. The message that the unrestrictedmodel conveys is that one also needs to purge the systematic response of taxes to government spending and demandshocks. Interestingly, this is also the assumption underlying Romer and Romer (2010)'s narrative approach to identifyexogenous changes in U.S. tax policy.

3.3. Unrestricted versus restricted measures of fiscal policy shocks

Using the estimates of the elements of A and the statistical innovations extracted in the first step of our estimationprocedure, it is straightforward to recover (via Eq. (2)) the time series of structural shocks and, in particular, fiscal policyshocks, implied by the unrestricted system and each of the restricted policy indicators discussed above. Fig. 5 depicts theunrestricted and restricted series of government spending shocks. Fig. 6 shows the series of tax shocks. Table 7 reports thecorrelation coefficients between the unrestricted and restricted measures of fiscal policy shocks.

25 A related argument is made by Rossi and Zubairy (2011), who point out that the exclusion of a measure of the interest rate from theeconometrician's information set may lead to incorrect identification of government spending shocks and their effects.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151138Fig. 5 shows that the time series of government spending shocks obtained under the restrictions associated with the Gindicator tracks very closely the unrestricted measure of shocks in each of the two sub-samples. The correlation between thetwo series is 0.99 in the first sub-period and 0.97 in the second (see Table 7). On the other hand, the time series of shocksobtained under the restrictions associated with the PD indicator are weakly correlated with their unrestricted counterparts,especially in the post-1979 period. This weak correlation reflects frequent and sometimes important gaps with respect tothe valid measures of government spending shocks. In particular, imposing the restrictions associated with the PD indicatorwould lead the econometrician to substantially underestimate the unexpected increase in public spending that occurredduring the Vietnam-War period (mid-1960s) and to completely miss the one that followed September 11, 2001. Theseresults are consistent with the test results discussed in the previous section and confirm that the primary deficit is a poorindicator of fiscal spending.

Regarding tax shocks, Fig. 6 reveals that the restrictions associated with the CAT indicator do not occasion any major mis-measurement of tax innovations in the pre-1979 period: the correlation between the restricted and unrestricted series ofinnovations is 0.98 in this sub-period (see Table 7). In the post-1979 period, however, these restrictions entail someimportant counterfactual implications, which explain their statistical rejection discussed in the previous section. Forexample, under these restrictions, one would mistakenly conclude that there were substantial exogenous tax cuts in 1994and tax increases in 1999. The restrictions associated with the PD indicator, for their part, generate a measure of tax shocksthat deviates markedly from the unrestricted one in both sub-samples, although the fit is much worse in the post-1979period. This again confirms that the primary deficit is not an appropriate indicator of tax policy.

Fig. 5. Government spending shocks. Solid lines: unrestricted measures, dashes: restricted measures.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 1393.4. Are fiscal policy shocks anticipated?

The SVAR approach has often been criticized on the ground that it may not be robust to fiscal foresight, i.e., thephenomenon that, due to legislative and implementation lags, future changes in fiscal policy are signaled to economic

Fig. 6. Tax shocks. Solid lines: unrestricted measures, dashes: restricted measures.

Table 7Correlations between the unrestricted and restricted measures of fiscal policy shocks.

Policy indicator Spending policy Tax policy

1960:11979:2 1979:32007:4 1960:11979:2 1979:32007:4

G 0.988 0.967 (0.005) (0.011)

CAT 0.984 0.808 (0.003) (0.030)

PD 0.669 0.115 0.841 0.807(0.151) (0.195) (0.032) (0.030)

Note: Figures between parentheses are standard errors.

agents several months before they become effective.26 To the extent that agents adjust their behavior in response toanticipated shocks, the resulting time series may have a non-invertible moving average component, such that it would beimpossible to recover the true fiscal shocks from current and past variables.27 Ramey (2011) presents suggestive evidencethat the SVAR-based innovations miss the timing of the news and are in fact predictable. More specifically, she shows thatthe government spending shocks extracted from a standard SVAR (identified via a Cholesky decomposition) are Granger-caused by Ramey and Shapiro's (1998) war dates.28

In order to investigate whether this criticism also applies to our government spending shocks, we subject them to theGranger causality test performed by Ramey. More precisely, we regress government spending shocks on four lags of adummy variable that represents the war dates, and test the joint significance of the regression coefficients. The results arereported in Panel A of Table 8. They indicate that the Ramey-Shapiro dates do not Granger-cause the (unrestricted)government spending shocks in any of the two periods.29 Evenwhenwe consider the shocks implied by the restricted policyindicators of fiscal spending, we find no evidence that they are Granger-caused by the war dates.30 We conclude that theSVAR government spending shocks correctly capture unexpected changes in public expenditures. One might suspect thatthis is the case because the effects of fiscal foresight are being impounded into the price of bonds and by conditioning onthis variable, we are able to capture the true conditioning set of agents. But we reach the same conclusion when we excludethe price of bonds from the system. This and the fact that the absence of Granger causality holds across several identificationschemes suggest that Ramey's findings are most likely driven by the Korean-War episode.

To undertake an analogous check for tax shocks, we use the dates isolated by Romer and Romer (2010) to identify

the time period and the specification. This means that these shocks are not forecastable based on the dates of legislatedexogenous tax changes.

Together, these findings suggest that the fiscal-foresight problem is not sufficiently severe to hinder the ability of the

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151140SVAR approach to correctly identify unanticipated fiscal policy shocks, at least conditional on the data used in this paper.32

This could be due to the fact that economic agents do not behave in a forward-looking manner, either because they aremyopic or because they are prevented from doing so (due, for example, to liquidity constraints). A more plausibleexplanation, however, is that an important fraction of fiscal policy shocks are in fact unanticipated.33 A recent study byMertens and Ravn (2012) lends support to this conjecture. Using artificial data generated by a neoclassical model withanticipated and unanticipated fiscal shocks, these authors show that the SVAR approach can successfully recover the trueimpulse responses to a unanticipated fiscal shocks provided that these shocks account for a relatively large fraction of thevariance of fiscal variables. Mertens and Ravn also estimate the effects of unanticipated government spending shocks in theU.S. using an augmented SVAR procedure that is robust to the presence of anticipated effects and find very similar results tothose obtained from a standard SVAR.34

4. Dynamic effects of scal policy shocks

In this section, we use system (7) to study the dynamic effects of unanticipated spending and tax shocks, and contrast theresults with those obtained by imposing the identifying restrictions commonly used in the literature.

26 Leeper et al. (2008) review the literature that reports reduced-form and anecdotal evidence on the extent of fiscal foresight.27 See Sims (1988), Hansen and Sargent (1991), Yang (2005), and Leeper et al. (2008).28 Ramey (2011) adds 2001:3 to the three episodes previously identified by Ramey and Shapiro (1950:3, 1965:1, 1980:1).29 This result is robust to using 1, 2 or 3 lags. We also considered the new military dates isolated by Ramey (2011) based on her reading of Business

Week and the New York Times, and found no evidence that these dates Granger-cause the SVAR government spending shocks. Likewise, we found noevidence that these shocks are Granger-caused by Fisher and Peters's (2010) accumulated excess returns of military contractors (graciously provided byJonas Fisher). The results are not reported but are available upon request.

30 The only exception occurs in the case of the PD indicator, for which government spending shocks are Granger-caused by the war dates in the1979:32007:4 period.

31 There are only two dates for which Romer and Romer report simultaneously tax changes taken for exogenous and endogenous reasons. Excludingthese two dates does not alter the outcome of our Granger-causality test.

32 Perotti (2004) also finds little evidence that the SVAR fiscal innovations are predictable in a sample of 5 OECD countries. More specifically, he showsthat these innovations are, in general, uncorrelated with the OECD forecasts of government spending and GDP growth.

33 As emphasized by Perotti (2004), throughout a given fiscal year, there are often supplements to the Budget and other decisions by the governmentsthat affect the outcome of fiscal policy. Moreover, Mertens and Ravn (2012) point out that of the 70 changes in the tax bill identified by Romer and Romer(2010) as being exogenous, 32 took effect within 90 days of the date on which they were legislated. In their empirical analysis, Mertens and Ravn treatthese tax changes as being unanticipated.

34 The augmented SVAR procedure, however, requires imposing additional identifying restrictions.exogenous changes in tax policy based on presidential speeches and Congressional reports. In Romer and Romer'sterminology, these exogenous changes correspond to legislated tax policy actions that are not taken for the purpose ofoffsetting factors that could affect output growth. Panel B of Table 8 reports Granger-causality results for the SVAR taxshocks. These results clearly show that Romer and Romer's dates do not Granger-cause the SVAR tax shocks, irrespective of

31

Table 8Granger causality tests.

Policy indicator A. Do Ramey & Shapiro's dates cause B. Do Romer & Romer's dates causeSVAR-based government spending shocks? SVAR-based tax shocks?

1960:11979:2 1979:32007:4 1960:11979:2 1979:32007:4

Unrestricted 0.157 0.422 0.807 0.518G 0.281 0.553 CAT 0.792 0.427PD 0.565 0.030 0.468 0.515

Note: Entries are the p-values of the F-distributed statistic used to test the joint significance of the coefficients in a regression of the SVAR-based shocks onfour lags of the dates.

Fig. 7. Dynamic responses to a government spending shock.

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 141

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 1231511424.1. Dynamic responses

Figs. 7 and 8 report the dynamic responses of output, government spending, taxes, the price of bonds, and the quantity ofbonds to a government spending shock and to a tax shock, respectively. In each case, the shock is normalized to itsunconditional standard deviation, i.e., unity. Since the quantity of bonds is not included in the SVAR, its response isconstructed residually using the government budget constraint.35 The figures also report (possibly asymmetric) 90%confidence intervals computed using the procedure developed by Sims and Zha (1999).36

Government spending shock: The upper panels of Fig. 7 show that, in both sub-periods, a positive government spendingshock leads to a temporary increase in output. The shape and the magnitude of the output response differ sharply, however,

Fig. 8. Dynamic responses to a tax shock.

35 The response of the quantity of bonds is constructed recursively using Rb;j Rb;j1Rq;jRg;jR;j and the initialization Rb;1 0, where Rx;j denotesthe response of variable x j periods after the shock.

36 Admittedly, the confidence bands reported in Figs. 7 and 8 are wide. However, we emphasize that such wideness is not induced by theheteroscedasticity approach to identification. We obtain similarly wide confidence intervals when we estimate the effects of fiscal policy shocks usingrecursive or BlanchardPerotti's identification schemes with conditionally homoscedastic shocks. These results are available upon request.

Table 9Fiscal multipliers.

System 1960:11979:2 1979:32007:4

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 143across the two periods: in the pre-1979 period, the increase in output is largest on impact and is statistically significant onlyat the time of the shock. In the subsequent quarters, the response becomes statistically insignificant. In contrast, in the post-1979 period, the response of output is persistent, mostly statistically significant, and hump-shaped, reaching its maximumat around 6 quarters after the shock.

As is common in the literature, we quantify the effects of government spending shocks on output by computing theassociated multiplier, which is defined as the dollar change in output that results from a dollar increase in the exogenouscomponent of public spending. Table 9 reports the value of the multiplier on impact, at the 4 quarter horizon and at thepeak. In the 1960:11979:2 period, the spending multiplier is 0.93 on impact and barely exceeds 1 at the peak. Thecorresponding numbers for the 1979:32007:4 period are 1.34 and 2.66, respectively. These numbers indicate that fiscalspending appears to have become more effective in stimulating economic activity after 1979.

Fig. 7 shows that taxes are initially essentially unresponsive to the government spending shock, suggesting that theincrease in spending is mostly financed by debt. Since the price of bonds decreases on impact in the first sub-period andremains roughly constant in the second, the government budget constraint implies that the quantity of issued bonds mustincrease in both cases (to finance the increase in public spending), which is what the lower panels of Fig. 7 show.

Tax shock: Fig. 8 depicts the dynamic responses to a positive tax shock. The upper panels of this figure show notabledifferences in the response of output across the two sub-periods. In the pre-1979 period, output remains inertial for aboutthree quarters after the shock before starting to fall in a persistent and statistically significant manner. After reaching atrough at around six quarters after the shock, output returns gradually to trend. This U-shaped pattern is much less apparentin the post-1979 period, where the unexpected increase in taxes leads to an immediate small increase in output followed bya very persistent, though statistically insignificant, decline.

Table 9 reports the values of the tax multiplier, defined as the dollar increase in output resulting from a dollar cut in theexogenous component of taxes. The tax multiplier is essentially zero on impact in the 1960:11979:2 period and evennegative in the 1979:32007:4 period. The maximum multiplier is larger in the former period than in the latter (0.84 versus0.51), but it is less than 1 in both cases. Importantly, we find that the tax multiplier is generally smaller than the spendingmultiplier, consistent with traditional Keynesian theory.37 Formally, the hypothesis that the spending and tax multipliers are

1Q 4Q Peak 1Q 4Q Peak

Spending policyUnrestricted 0.927 0.037 1.028 (3) 1.342n 2.151n 2.656n (7)Cholesky 1.192n 0.121 1.194n (3) 0.887n 1.645n 2.232n (7)Blanchard and Perotti 1.279n 0.226 1.279n (1) 0.951n 1.737 1.985 (7)Tax policyUnrestricted 0.039 0.682 0.843n (6) 0.280 0.161 0.509 (12)Blanchard and Perotti 0.082 0.525 1.036n (8) 0.044 0.066 0.780 (15)

Notes: The multiplier is defined as the dollar change in output at a given horizon that results from a dollar increase (cut) in the exogenous component ofgovernment spending (taxes). An asterisk indicates that the 90% percent confidence interval does not include 0. Figures between parentheses indicate thequarters in which the maximum value of the multiplier is attained.equal cannot be rejected at any given horizon in the pre-1979 period. In contrast, the difference between the two multipliersis statistically significant for the first sixteen quarters (except the second) in the post-1979 period. This result stands incontrast to that reported by Mountford and Uhlig (2009) who find that tax cuts are more effective than increases ingovernment spending to boost the economy.

Fig. 8 shows that a second discrepancy in the results across the two periods concerns the response of governmentspending, which is positive in the pre-1979 period but negative after 1979. None of these responses, however, is statisticallydistinguishable from 0. Thus, our results provide little support for the so-called starve-the-beast hypothesis, which statesthat tax cuts should lead to a reduction in future government spending. Romer and Romer (2009) have recently emphasizedthe importance to test this hypothesis using exogenous measures of taxes to avoid biases due to inverse causation andomitted variables. Using the narrative records to isolate legislated tax changes that are unlikely to be correlated with otherfactors affecting government spending, they also find little evidence in favor of the starve-the-beast hypothesis.

The price of bonds also responds asymmetrically across the two sub-samples, rising significantly in the pre-1979 periodand falling in the post-1979 period. In both cases, however, the initial increase in taxes is so large (relative to the response ofgovernment spending and the price of bonds) that the quantity of issued bonds falls after the shock.

37 The only exception occurs at the four-quarter horizon in the pre-1979 period.

4.2. Comparison with the restricted systems

It is instructive to assess the implications of imposing the various sets of identifying restrictions discussed in Section 2.2.More specifically, the purpose of this section is to determine whether these restrictions lead to significant differences in thevalues of the spending and tax multipliers relative to those obtained from the unrestricted system.38 Starting with thespending multiplier, Table 9 shows that the Cholesky and BlanchardPerotti identification schemes overestimate the effects

At this stage, it is useful to recall that, in recursive systems or in Blanchard and Perotti's SVAR, the size of the tax

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151144multiplier is entirely determined by , for a given (unconditional) covariance matrix of the statistical residuals (see Caldaraand Kamps, 2012). However, because our SVAR allows for contemporaneous interaction between all the variables of interest,the remaining parameters of the matrix A do affect the response of output to tax shocks, and therefore play an importantrole in determining the size of the tax multiplier. To illustrate this point, we have computed the tax multiplier (as a functionof implied by the two following systems:

~a11 ~a12 ~a12= 0~a21 ~a22 ~a23 00 ~a33 ~a33 00 0 0 ~a44

0BBBB@

1CCCCA

vg;tvy;tv;tvq;t

0BBBB@

1CCCCA

g;t

1;t;t

d;t

0BBBB@

1CCCCA; 21

and

~a11 ~a12 ~a12= 0~a21 ~a22 ~a23 ~a240 ~a33 ~a33 00 0 ~a43 ~a44

0BBBB@

1CCCCA

vg;tvy;tv;tvq;t

0BBBB@

1CCCCA

g;t

1;t;t

d;t

0BBBB@

1CCCCA: 22

Although system (21) includes the price of bonds, it yields identical effects of a tax shock to those implied by Blanchard andPerotti's SVAR. Hence, this system implies that the tax multiplier is only a function of and not of any other structuralparameter. In contrast, system (22) relaxes the restriction ~a24 0, but imposes a value on the parameter ~a43 (in order toachieve identification under conditional homoscedasticity). We consider two cases ~a43 21:15 and ~a43 21:15.40 Asshown in Fig. 9, the value of the tax multiplier implied by system (22) depends not only on but also on the calibratedvalue of ~a43. This implies that the same value for the tax multiplier could be obtained with different values of :

5. Extensions

Having analyzed the effects of fiscal policy shocks on aggregate output, we now investigate how these shocks affectprivate consumption and investment. This exercise is useful on two counts. First, it helps determine which type of privateexpenditure is more responsive to fiscal policy, thus allowing a better understanding of the channels through which fiscalinstruments affect aggregate output. Second, the response of private consumption to unanticipated changes in governmentspending is useful to discriminate between competing views of fiscal policy: According to Keynesian theory, an increase ingovernment spending should lead to an increase in consumption, whereas standard neoclassical models predict that publicspending crowds out consumption due to a negative wealth effect (Barro and King, 1984 and Baxter and King, 1993). Whilemost of existing studies using SVARs tend to corroborate the crowding-in effect, the magnitude of this effect is sensitive

38 Since the PD indicator is found to be strongly rejected in the data in both sub-samples, we shall not discuss it any further.39 For the sake of remaining as faithful as possible to the original specification of Blanchard and Perotti (2002), the results based on their model are

generated using a three-variable VAR that includes output, government spending and taxes. This is the reason why those results differ from the onesimplied by the Cholesky scheme. As is well known, with the same set of variables, and as long as government spending is placed first in the SVAR, systemswith a bloc-recursive A matrix, such as purely recursive systems or those imposing BlanchardPerotti's restrictions, yield identical dynamic responses to agovernment spending shock, and hence identical values for the spending multiplier.

40 These values are inspired by our unrestricted estimates for the post- and pre-1979 periods, respectively.of government spending shocks on output in the 1960:11979:2 period and underestimate them in the 1979:32007:4period. Under these two schemes, the spending multiplier is larger than 1 on impact in the pre-1979 period but is below 1 inthe post-1979 period, which is the opposite of what the unrestricted system predicts.39 Interestingly, the bias in theestimated value of the spending multiplier is larger in the post-1979 period than before 1979. This observation is consistentwith the fact that the identifying restrictions implied by the Cholesky and BlanchardPerotti schemes are soundly rejectedby the data in the post-1979 period, whereas they can only be rejected at the 8.5 percent significance level or higher in thepre-1979 period (see Panel C of Table 6B).

Table 9 also reveals that the tax multiplier implied by the BlanchardPerotti identification scheme is significantly largerthan that predicted by the unrestricted approach in both sub-samples. For example, the former yields a peak multiplier of1.04 in the pre-1979 period and 0.78 in the post-1979 period, whereas the corresponding numbers are 0.84 and 0.51 in theunrestricted system.

0.6

0.8

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151 145to identification. Furthermore, this effect may well vanish altogether if one relaxes the commonly used identifyingassumptions.

To examine the implications of our unrestricted SVAR for consumption and investment, we extend the estimated systemby adding each of these two variables one at a time. The implied dynamic responses of consumption to governmentspending and tax shocks are reported in Fig. 10. The corresponding results for investment are shown in Fig. 11.

5.1. Consumption

Following an unexpected increase in government spending, private consumption exhibits a muted and statisticallyinsignificant response at all horizons in the pre-1979 period. In contrast, it reacts positively and persistently to the shockafter 1979. For this sub-period, the consumption response is similar to that of output, being hump shaped and statisticallysignificant during the first six quarters after the shock. Thus, at least in the post-1979 period, there is clear evidence of a

eta_tau

multip

lier

-5.0 -2.5 0.0 2.5 5.0-0.8

-0.6

-0.4

-0.2

-0.0

0.2

0.4

Fig. 9. Tax multiplier as a function of . Solid line: BlanchardPerotti, dotted line: alternative system with ~a43 21:15, and dashed line: alternativesystem with ~a43 21:15.crowding-in effect of public spending on private consumption, contrary to neoclassical theory.41

In the pre-1979 period, an unanticipated increase in taxes lowers private consumption, but with a delay of severalquarters. The consumption response is statistically significant in a window of 511 quarters after the shock and reaches itstrough at around 7 quarters after the shock. In the post-1979 period, the increase in taxes also lowers consumption, but theeffect is statistically significant only during the first four quarters after the shock. Thus, tax shocks appear to have more rapideffects on consumption in the post-1979 period than before 1979.

5.2. Investment

According to the point estimates in the top panels of Fig. 11, a positive government spending shock initially raises totalinvestment both in the pre- and post-1979 periods. In both sub-samples, however, the increase is short lived and statisticallyinsignificant at any given horizon except at the time of the shock in the post-1979 period. In other words, there is noevidence that public spending shocks crowd in or out private investment.

In response to an unanticipated increase in taxes, private investment exhibits a persistent and non-monotonic decline inboth sub-periods, with a trough occurring at around four to five quarters after the shock. Before 1979, however, theinvestment response is statistically different from zero only at impact and at the trough, whereas it remains statisticallysignificant for about eleven quarters in the post-1979 period.

Overall, these results indicate that while both components of private spending, i.e., consumption and investment,respond to public spending and tax shocks, the effect of fiscal policy on aggregate output is largely determined by theresponse of private consumption.

41 Several explanations have been proposed to reconcile theory with data. Most of these explanations operate through consumer preferences (Bouakezand Rebei, 2007; Ravn et al., 2007; Monacelli and Perotti, 2008). Gal et al. (2007), on the other hand, propose a resolution that emphasizes the interactionof sticky prices, non-Ricardian consumers and a non-competitive labor market.

Resp. of consumption

-0.0050

0.0100Resp. of consumption

-0.0050

0.0100

5 10 15 20 5 10 15 20

H. Bouakez et al. / Journal of Economic Dynamics & Control 47 (2014) 123151146Resp. of consumption

Tax

shoc

k

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006Resp. of consumption

Tax

shoc

k

5 10 15 20 5 10 15 20-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006Gvt

Spe

ndin

g S

hock

-0.0025

0.0000

0.0025

0.0050

0.0075

Gvt

Spe

ndin

g S

hock

-0.0025

0.0000

0.0025

0.0050

0.00756. Misspecication Issues

As stated above, the structural model underlying our empirical framework, represented by Eqs. (3)(6), is purposely keptsimple in order to impose as few restrictions as possible on the data. However, that model may be criticized on the groundsthat (i) its equations are not derived from first principles and may violate the cross-equation restrictions that amicrofounded theory would imply, and (ii) it does not guarantee a non-explosive path for public debt as the government'sintertemporal budget constraint (transversality condition) is not explicitly imposed and no restriction is placed howgovernment spending and taxes respond to past public debt. These considerations may raise concerns about the possibilitythat the model is misspecified which may result in a mis-measurement of