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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
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/jedc
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: [email protected] (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
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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.
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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.
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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).
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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