Impact of Temporary Fiscal Shocks on the
Canadian Economy
Jean-Philippe Cayen
Bank of Canada
Hélène Desgagnés
Bank of Canada
Preliminary version, April 2009
Abstract
In this paper, we assess the e¤ects of temporary …scal shocks on
the Canadian economy using the structural vector autoregression approach. We consider distinct shocks to government spending and tax
revenues, and we confront three types of identi…cation approaches.
The …rst one is the recursive approach based on the Cholesky decomposition. The second approach follows Blanchard and Perotti (2002)
and Perotti (2004) who employed elasticities estimated using information on the tax system to identify the VAR model. In the last one,
we impose restrictions on the sign of the variables’ responses to the
shocks along the lines of Mountford and Uhlig (2005). We …nd that
the e¤ects of the government revenues shock are more robust across
the identi…cation approaches than the shock to government expenditures. For all the identi…cation approaches, the shock to government
expenditures has a bigger impact on GDP than the net tax revenues
shock in the very short run. However, on a horizon of two years, the
revenues shock dominates because it has a larger stimulating e¤ect
on the other components of GDP. In light of our …ndings, we view
a speci…cation of the Blanchard and Perotti (2002) model in which
the zero output elasticity of government expenditures assumption is
dropped as the one leading to the most credible results.
JEL classi…cation: E60, E62, H20, H50
Bank classi…cation: ...
The views expressed in this paper are those of the authors. No responsibility for them
should be attributed to the Bank of Canada.
1
Introduction
The vector autoregression (VAR) methodology has become an important
empirical tool for studying the e¤ects of …scal policy in recent years. For instance, the structural VAR model developed by Blanchard and Perotti (2002)
is one of the most cited works on the topic. One of the major issues when
working with a VAR model is to choose an appropriate approach to identify
the structural shocks. To study the e¤ects of …scal policy using a VAR, we
have to make the distinction between random discretionary …scal shocks and
…scal policies that respond to the economic situation in a systematic way,
such as the employment insurance bene…ts or the taxes on revenue.
Besides the Blanchard-Perotti approach, other identi…cation strategies
have been proposed to disentangle these two aspects of …scal policy such
as the recursive approach (Fatas and Mihov, 2001) and the sign restrictions
approach (Mountford and Uhlig, 2005). Unfortunately, all approaches do
not yield the same results. For example, while most studies agree that a
positive government spending shock will have a positive impact on GDP
in the United States (see Blanchard and Perotti, 2002), this e¤ect is not
always signi…cantly di¤erent from zero (see Perotti, 2004). There is not
even a consensus whether an unexpetected tax cut will have a positive or a
negative impact on the economy (see Perotti, 2004). Likewise, most of the
empirical work on …scal policy has been done with U.S. data. Perotti (2004),
and Phaneuf and Wasmer (2005) are among the few who have dealt with
Canadian data in the VAR framework.
The goal of our paper is to assess the e¤ects of temporary government
spending and revenues shocks on the Canadian economy. For this purpose,
we construct a VAR model and we compare the results we obtain using three
identi…cation approaches: the recursive approach, the Blanchard-Perotti approach and the sign restrictions approach.
We …nd that the e¤ects of the government revenues shock are more robust
across the di¤erent identi…cation approaches than the shock to government
expenditures. An unexpected decrease of net tax revenues causes a gradual increase in real output, no matter which approach we use. The results
are less consistent following the government spending shock. With the sign
restrictions approach, a positive shock to government expenditures will be
followed by a sustained increase of real GDP, while with the recursive and the
standard Blanchard-Perotti approaches, the same shock generates a modest
increase of output that lasts only one quarter.
1
In the next section, we brie‡y review previous work using various VAR
models to study the e¤ects of …scal policies. Then, we describe our VAR
model as well as the di¤erent approaches we test. In the last two sections,
we present our results and discuss di¤erent robustness issues.
2
Literature Review
Many papers deal with the impacts of …scal policies using VAR models. In
most papers, the authors distinguish the impact of spending and revenues
shocks instead of working only with the budgetary balance. This is probably
explained by the fact that we expect the impacts to be di¤erent whether the
government decides to cut the taxes or to increases spending.
The recursive approach presented in Fatas and Mihov (2001), and Gali
et al. (2007) restricts the matrix linking the reduced-form residuals to the
structural shocks to be lower triangular to achieve identi…cation. As a result,
the order of the variables in the model is crucial. Both papers …nd that the
spending shock has a positive and signi…cant e¤ect on the level of output.
Fatas and Mihov …nd a maximal multiplier impact of three.
To reduce the number of zero restrictions imposed by the recursive strategy, Blanchard and Perotti (2002) incorporate external information on the
tax system in their VAR to identify the shocks. They also …nd that the
spending shock has a positive and signi…cant impact on the U.S. economy.
On the contrary, a positive tax shock has a negative cumulative e¤ect on
GDP.
The sign restriction approach has been popularized by Uhlig (2005) who
implemented it to evaluate the e¤ects of monetary policy shocks. Mountford
and Uhlig (2005) use it to assess the e¤ects of …scal policy shocks on the U.S.
economy. The idea is to restrain the direction of the responses to a speci…c
shock in a way that is coherent with economic theory. It is somehow less
restrictive than the two previous approaches since it does not impose any
speci…c value for the models’s coe¢ cients. On the other hand, imposing a
signi…cant positive (negative) response of variables for many quarters could
lead to upward (or downward) biased estimates. This approach leads to
slightly di¤erent results than the recursive and the Blanchard and Perotti
approaches. The rise in GDP following the spending shock is smaller than
in previous papers. On the other hand, the tax shock as a signi…cant impact
on GDP as Blanchard and Perotti (2002) …nd.
2
Since the results for the U.S. economy di¤er across the di¤erent papers
cited above, Caldara and Kamps (2008) revisit all approaches to investigate
whether the di¤erences are due to various reduce-form speci…cations or different de…nitions of the data. They conduct their experiment with the same
set of American data than Perotti (2004). They …nd that the spending shock
has a positive impact on GDP. The response to a negative revenues shock is
close to zero when they use the recursive or Blanchard-Perotti approaches,
but positive with the sign restriction approach.
Perotti (2004) extends the Blanchard-Perotti approach to …ve OECD
countries - including Canada - and he …nds substantial di¤erences in estimated impacts of …scal shocks across countries. As a results, conclusions of
previous work using U.S. data can hardly be transposed to Canada. Besides
Perotti (2004), Phaneuf and Wasmer (2005) also use a VAR estimated with
Canadian data. Perotti (2004) …nds a very modest response of GDP to the
…scal shocks. Furthermore, the reponses depend on the subsample used to
perform estimation. The estimated impact in Phaneuf and Wasmer (2005)
is signi…cantly di¤erent from zero, but still modest.
Alternative empirical tools have also been used to study the impact of …scal policies. As an example, Murchison and Robbins (2003) estimate an indicator of …scal policy stance by the generalized method of moments approach.
This work is of a particular interest for us because they estimate the output
elasticities of …scal variables, which can be used in a VAR model. However,
their methodology is suitable for an assessment of permanent shocks. And,
further, it does not bene…t from the dynamic framework of a VAR.
3
Methodology
Similar to Blanchard and Perotti (2002) and to Phaneuf and Wasmer (2005),
we use a three variables speci…cation for our base case VAR. Other authors
like Fatas and Mihov (2001), Mountford and Uhlig (2002), Perotti (2004),
Gali et al. (2007), and Caldara and Kamps (2008) use more variables in their
model, but such a strategy generally requires the imposition of less realistic
restrictions to identify the shocks. Nonetheless, we also present a sensitivity
analysis that compares the results from alternative speci…cations to our base
case results.
The remainder of this section is divided into two parts. In the …rst one,
we present the data used, while in the second part, we describe the three
3
identi…cation approaches we use in this paper. The discussion around the
additional variables and restrictions needed for the speci…cation involving
more than three variables will be made in the section 5 where we present the
sensitivity analysis.
3.1
Data
Our base case VAR contains one measure of economic activity, real Canadian
GDP (yt ), and two …scal variables - real government expenditures (Gt ) and
real net tax revenues (Tt ) - to re‡ect the fact that the government can use
either spending or revenue policies to in‡uence the economy. The sample
goes from the …rst quarter of 1961 to the second quarter of 2008.
The …scal variables, as well as real GDP, come from the National Income
and Expenditure Accounts published by Statistics Canada. Our measure of
real government expenditures corresponds to the sum of government current
expenditure on goods and services, government gross …xed capital formation,
and government investment in inventories. Net tax revenues include the
sum of taxes on incomes, contributions to social insurance plans, taxes on
production and imports, and other transfers from persons minus current
transfers to persons and business. We do not account for interest payments
on the public debt because the …scal authorities have little in‡uence on this
variable in the short term. Since the components of the net tax revenues
are only published in nominal terms, we de‡ate them with the government
expenditure de‡ator.1
The series are seasonally adjusted and they are all de‡ated by the Bank
of Canada’s estimate of potential output.2 We assume that potential output
does not respond to temporary shocks identi…ed in the VAR. It should be
noted that important low frequency movements remain present in the ratios
of real government expenditures to potential output and of real net tax revenues to potential output (see Figure 1). In fact, augmented Dickey-Fuller
1
The series come from Statistics Canada database CANSIM. The mnemonic for real
GDP is v1992067. The mnemonic of the components used to construct real government
expenditures are v1992049, v1992050, and v1992051. The mnemonic of the components
of net tax revenues are v498317, v498321, v498322, v498323, and v49328. The mnemonic
of the serie used to de‡ate net tax revenues is v1997743.
2
Butler (1996) describes the extended multivariate Filter (EMVF) used at the Bank
of Canada to estimate potential output. A subsample of the potential output serie is
available on the Bank of Canada website.
4
tests show that these two series are non-stationary. In both series, there
seem to be two distinct shifts in the mean of the series. For the ratio of real
government expenditures to potential output, the shifts happen around 1980
and 1994, while for the ratio of real net tax revenues to potential output,
these shifts seem to happen in 1974 and in 1986. In our view, those low frequency movements re‡ect permanent discretionary policy changes made by
successive governments over time. As described in Blöndal (2001), Kneebone
and McKenzie (1999), and Traclet (2004), …scal policy in Canada has substancially evolved over time. For example, important tax cuts and increases
in subsidies in the mid-70s reduced government’s net revenues. This period
also marked the beginning of successive de…cits. Some changes in …scal policy occurred in the 80s on the budget formulation (1980) as well as on the
taxes side (1986) to reduce de…cits with more or less success. By the end of
the 80s and early 90s, the de…cit reduction had become a major issue and
strong policies had been implemented to create a healthier …scal climate.
To account for these regime shifts we detrend the two …scal ratios in the
VAR using a HP …lter ( = 20 000). The orginal and detrended series, as well
as the gap between them are illustrated in the Figure 1. Other detrending
methods are presented in the sensitivity analysis of section 5. We detrend the
series because we want to capture only the e¤ects of temporary …scal shocks.
If we were not detrending the series, the estimated stochastic shocks would
be linear combinations of temporary and permanent shocks. This would not
be a problem if temporary and permanent shocks had similar e¤ects on the
economy, but theoretical models usually show that this is not the case (see,
among others, Baxter and King, 1993).
Blanchard and Perotti (2002), Perotti (2004) and Caldara and Kamps
(2008) also detrend the series they use. However, they detrend all the variables of their model, even real output, with simple deterministic time trends.
For Canada, the assumption of a deterministic time trend is problematic
because there has been important changes in the growth rate of potential
output over time, as shown in Cayen and van Norden (2005). This means
that the output gap would remain non stationary even after it has been detrended with a time trend. This is why we use an alternative approach to
detrend real GDP and the other variables.
5
3.2
The VAR and the identi…cation approaches
We express the reduced-form version of the VAR as:
Xt = A (L) Xt
1
+ Ut
(1)
where Xt = [yt ; Gt ; Tt ] is the three-dimensional vector of endogenous variT
ables, Ut = [uyt ; uG
t ; ut ] is the corresponding three-dimensional vector of
reduced-form residuals, and u = Ut Ut0 is the variance-covariance matrix
of the system. The VAR contains two lags as suggested by the likelihood
ratio tests and no constant or other deterministic variable since the series
are already detrended.3
We use the same structural VAR representation than Caldara and Kamps
(2008):
A0 Xt = A0 A (L) Xt
1
+ BEt
(2)
where A0 represents the contemporaneous relation among variables. Assuming that BEt = A0 Ut , one simply needs to pre-multiply (2) by A0 1 to retrieve
the reduced form (1).
This brings us to the topic of identifying the structural shocks. In the
T
VAR literature, the structural shocks, Et = ["yt ; "G
t ; "t ], are usually assumed
to be uncorrelated with each other, which means that the variance-covariance
matrix of the structural shocks ( " = Et Et0 ) is diagonal. Since A0 , B, and
the diagonal elements of " are not identi…ed, we need to impose restrictions
on these matrices to identify the structural shocks. In this paper, we test
three di¤erent approaches that have been used in the literature to identify
…scal shocks.
3.2.1
The recursive approach
The recursive approach requires B from equation (2) to be an identity matrix
and A0 to be a lower triangular matrix with a unit diagonal. This approach
assumes a causal ordering of the variables of the model. We follow Fatas and
Mihov (2001), Gali et al. (2007), and Caldara and Kamps (2008) who ordered
government expenditures …rst, followed by output, and net tax revenues.
3
Likelihood ratio tests show that higher order VARs up to eight lags are not signi…cantly
di¤erent than a two lags VAR, while the two lags speci…cation outperforms the one lag
speci…cation.
6
This implies the following relationship between the reduced-form residuals
Ut , and the structural shocks Et :
2
32 3 2
32 3
1
0
0 uG
1 0 0 "G
t
t
4 yG
1
05 4 uyt 5 = 40 1 05 4 "yt 5
(3)
T
T
ut
0 0 1
"t
TG
Ty 1
This ordering implies that government expenditures do not respond contemporaneously to shocks to other variables, while real output does not react
contemporaneously to revenues shocks. In the three variables framework,
the restrictions concerning the reaction of government expenditures seem
plausible because government spending is in principle largely unrelated to
the business cycle. It is true that the government could decide to implement
systematic countercyclical policies when they observe major shocks a¤ecting
the economy, but there is no automatic stabilizer among the components of
government expenditures, so it is fair to assume that it would take at least
one quarter before government realizes that there is a shock in the private
sector, and reacts to it.
Assuming the absence of reaction of real output to tax shocks is probably
less realistic than the two previous restrictions, but it would be even less
credible to assume that net tax revenues do not react contemporaneously to
other shocks in the economy because of the numerous automatic stabilizers
in the tax system. Consequently, we order GDP second.
3.2.2
The Blanchard-Perotti approach
Blanchard and Perotti (2002) highlight that unexpected movements in govT
ernment expenditures (uG
t ) and in net tax revenues (ut ) can be explained
by three distinct factors: the responses to unexpected movements in GDP
(uyt ), to structural shocks to spending ("G
t ), and to structural shocks to net
T
tax revenues ("t ). They also state that unexpected movements in GDP (uyt )
can be due to unexpected movements in government expenditures (uG
t ), or
in net tax revenues (uTt ), or to other unexpected structural shocks ("yt ). This
can be written as the following system of equations:
uG
t =
y
Gy ut
+
T
GT "t
+ "G
t ;
(4)
uTt =
y
T y ut
+
G
T G "t
+ "Tt ;
(5)
uyt =
G
yG ut
+
T
yT ut
+ "yt :
(6)
7
The above system is not identi…ed. Blanchard and Perotti rely on institutional information about tax, transfer, and spending programs of the U.S.
economy to set the parameters Gy and T y . With these two parameters, they
construct the cyclically adjusted reduced-form residuals of government exy
y
T
T
penditures and of net tax revenues: utG = uG
Gy ut and ut = ut
T y ut .
t
and uTt are no longer correlated with "yt , they can use them as
Since uG
t
T
instruments to estimate yG and yT in a regression of uyt on uG
t and ut . To
complete the identi…cation of the model, they must either calibrate GT to
estimate T G , or calibrate T G to estimate GT .
Perotti (2004) applies that approach on …ve OECD countries, including
Canada. For all the countries, he sets the output elasticity of government expenditures ( Gy ) to zero, since there is no evidence of any automatic response
of government spending to changes in GDP within a quarter. To estimate
the output elasticity of government revenue, Perotti regresses individual revenue items (individuals and corporate income taxes, social security taxes,
indirect taxes, transfers) on their respective tax base and aggregate them
together. For Canada, his estimate of the output elasticity of government
revenue ( T y ) is 1:86.
Murchison and Robbins (2003) also estimate the output elasticities of
government revenue and transfers, but with a di¤erent approach than Perotti (2004). They also report more disaggregate information than Perotti.
Their estimates ‡uctuate between 1:65 for personal income taxes and 2:03
for corporate income taxes and indirect taxes, which is similar to Perotti’s
estimate. Contrary to Perotti (2004) who calibrates the output elasticity
of government expenditures ( Gy ) to zero, Murchison and Robbins (2003)
estimate it at 0:9.
For our work, we report two sets of results for the Blanchard-Perotti
approach. In the …rst one, we use Perotti’s (2004) estimates of the the output
elasticities of government revenue and expenditure , while for the second one,
we use the estimates of Murchison and Robbins (2003).
Since we are not working with the log of government expenditures and
of net tax revenues as Perotti, but with their level (de‡ated by potential
output), we must modify the value of Gy and T y to make sure that it is
compatible with the type of data we are working with.4 Perotti estimates
4
As an example, the output elasticity of government revenue corresponds to
T =T0
=
Y =Y0
8
T y:
of Gy and T y become 0 and 0:43 respectively, and Murchison and Robbins
estimates become 0:21 and 0:43 respectively.
Perotti shows that the results are similar whether he sets GT = 0 or
T G = 0. Since our results are also similar whether we assume GT = 0 or
T G = 0, and because it is also the assumption that is made in the recursive
approach, we assume that GT = 0. This is equivalent to say that government
expenditures are una¤ected contemporaneously by government decisions on
the revenue side. Coming back to the contemporaneous relationship between
the structural shocks (Et ) and the reduced-form residuals (Ut ) in equation (2),
the restrictions implied by the Blanchard-Perotti approach can be written as:
2
3 2 G3 2
3 2 G3
1
0
ut
1 0 0
"t
Gy
y5
4 yG
5
4
4
5
4
1
u
0
1
0
"yt 5
=
(7)
yT
t
T
T
0
0:43
1
ut
"t
TG 0 1
where Gy equals 0 in Perotti’s speci…cation and 0:21 in the speci…cation
based on Murchison and Robbins (2003).
3.2.3
The sign restrictions approach
Lastly, we follow Mountford and Uhlig (2005) who impose sign restrictions
on the impulse responses to identity …scal shocks. Their key assumption
is that, following a positive business cycle shock that push real GDP up
for at least four quarters, net tax revenues should increase for at least four
quarters because of the automatic stabilizers. They also assume that all
shocks orthogonal to the business cycle shock are discretionary …scal policy
shocks. Mountford and Uhlig make the distinction between three types of
…scal shocks: the “de…cit spending shock” is identi…ed as increasing government expenditures but leaving government revenue unchanged for the
four-quarters window following the shock; the “revenue shock” is identi…ed
Because our variables are not log-transformed, we are concerned by the impact of
T . Therefore, what matter for us is
Tt
=
Yt
T0
Y0
Y on
T y:
For G0 , T0 and Y0 , we take respectively the average value of the ratio of government
expenditure to potential output (0:23), of the ratio of government revenu to potential
output (0:23), and of the ratio of real GDP to potential output (1:0) over the entire
sample.
9
as increasing government net tax revenue but leaving government expenditures unchanged; and the “balance budget spending shock” is identi…ed by
requiring both government expenditures and revenues to increase in such a
way that the budget remains balanced. They assume that the three …scal
shocks are orthogonal to each other.
We apply the same sign restrictions than Mountford and Uhlig (2005) to
identify a non-…scal shock, a spending shock, and a …scal revenues shock,
except that we force the response to each …scal variable to the shock of the
other …scal variable to be equal to zero for only one quarter. We do not try to
identify a balanced budget spending shock for two reasons. First, contrary to
Mountford and Uhlig (2005), our VAR contains only three variables, so it is
not possible to identify more than three structural shocks. Second, we view
the discretionary …scal shocks as a deliberate attempt to stimulate or to slow
the pace of the economy. It is hard to imagine the government trying to do
this without letting the budget balance moving. Restrictions are summarized
below:
2 3 2
3 2 G3
Gt
+
0
"t
4 yt 5 = 4
5 4 "yt 5 :
+
(8)
Tt
0 +
"Tt
Paustian (2006) demonstrates that, in order to uniquely identify a structural shock using a sign restrictions identi…cation approach, the number of
restrictions imposed need to be larger than the number typically imposed in
recent studies, and the variance of the shock of interest relative to the other
shocks of the model must be large enough to ensure that the shock is the major source of ‡uctuations. Based on Paustian criticism, we believe Mountford
and Uhlig do not impose enough restrictions to uniquely identify the shocks.
For example, we could face a situation where government expenditures do
not react to business cycle shocks and where GDP reacts negatively to what
is supposed to be a negative government revenue shock. In such a case, we
could not tell which shock is the business cycle shocks and which one is the
…scal shock.
To account for this criticism, we consider a second speci…cation with a
larger number of restrictions. Since we are interested in the impacts of more
than one shock, we cannot met the condition concerning the relative size of
the variance. Nevertheless, Paustian (2006) also shows that if a su¢ ciently
large number of restrictions is imposed, we don’t need to care about the
relative size of the variances of the shocks.
10
For the positive business cycle shock, we impose that the budgetary balance, namely the di¤erence between government net revenues and spending,
be positive for four quarter following the shock, in addition to the restrictions
imposed by Mountford and Uhlig (2005). This is consistent with the government trying to reduce the debt level when the economy is growing above
potential. To distinguish the business cycle shock from the two …scal shocks,
we impose for the …scal shock that GDP moves in the opposite direction than
the budgetary balance. This assumption may be too strong, especially for
the revenues shock which may not a¤ect real GDP depending on the saving
habit of consumers and …rms, but it is the only way we can make sure we
properly di¤erentiate the …scal shocks from the business cycle shock. Finally,
we do not impose that the …scal spending shock has no impact on government revenue like Mountford and Uhlig (2005) do because of the e¤ect of the
automatic stabilizers. On the other hand, we do impose that the …scal shock
to government revenue has no immediate impact on government expenditure
since there are no obvious automatic stabilizers on the spending side. The
restrictions for the alternative sign restrictions approach are illustrate by the
following equation:
2
3 2
3
Gt
+
0 2 G3
6
7 6+ + +7 "ty
yt
6
7=6
7 4 "t 5 :
(9)
4
5 4
5 T
Tt
+
"t
(Tt Gt )
+
To implement the sign restrictions approach, we follow the procedure proposed by Rubio-Ramírez et al. (2005). Their starting point is any exactly
identi…ed structural VAR of the form of equation (2). The results are independant of the approach used to identify the structural shocks, as long as
the shocks are orthogonal between each others and as long as the VAR is not
overidenti…ed. The goal is to …nd an orthogonal matrix P of dimension k (in
our case, we need a 3 3 matrix) such that when we pre-multiply equation
(2) by this matrix,
P A0 Xt = P A0 A (L) Xt
1
+ P BEt ;
(10)
the impulse responses resulting from this new system of equations satisfy the
sign restrictions. To create a P matrix, Rubio-Ramírez et al. (2005) generate
a random matrix Z (each element of Z follows an independent standard
normal distribution), which they decompose with the QR decomposition.
11
Their P matrix corresponds to the orthonormal Q matrix resulting from this
QR decomposition of Z.
Of course, not all randomly generated Z matrices will result in a P matrix
satisfying the sign restrictions. Rubio-Ramírez et al. (2005) use a four steps
algorithm that helps obtaining impulse responses that satisfy all the sign
restrictions.
Step 1. Let (A0 ; A(L); B; " ) be a draw from the posterior distribution of
any exactly identify structural VAR of the form of equation (2).
Step 2. Draw an independent standard normal 3
Z = QR be the QR decomposition of Z:
3 matrix Z; and let
Step 3. Let P = Q, and generate the impulse responses from the system of
equations (10).
Step 4. If these impulse responses do not satisfy the sign restrictions, return
to step 2.5
The resulting outcome of this four step algorithm (P A0 ; P A(L); P B; " )
constitute the posterior draw of the structural parameters of the structural
VAR with sign restrictions. For this work, we generate 1000 draws from the
posterior distribution.
3.3
Bayesian framework
We use a Bayesian framework because the sign restrictions approach and
the method for drawing error bands proposed by Sims and Zha (1999) both
involve Bayesian techniques.
The Bayesian theory considers parameters as random variables and the
priors re‡ect the uncertainty around those values before observing the data.
Once we observe the data, priors may change and the new information is
contained in the posterior density. Sims and Zha rely on this posterior probability in drawing error bands.
We use the Normal-Wishrat prior for (A (L) ; u ) as suggested in Uhlig
(1994) and Monte Carlo based numerical simulation techniques to simulate
draws from the posterior density. We take 1000 draws from the posterior
density to draw error bands.
5
Since we cannot impose a precise value for the zero restrictions, we restrict the response
to be within the 1:0 10 4 interval.
12
4
Results
In this section, we present the responses of real GDP and the two …scal
variables to the non-…scal shock, the shock to government revenues and the
shock to government expenditures we obtain with the three identi…cation
approaches described in the previous section. Since we work with the level
of the variables de‡ated by potential output, and we assume that potential
output does not respond to the shock identi…ed in the VAR, our impulse
responses report the movements of the series in dollar term. We normalize
the impact of each shock such that a variable increases by one dollar following
its own shock.
In the …gures reporting the results, "RA" stands for the recursive approach, "BP1" for the Blanchard-Perotti approach with Perotti’s (2004) estimates of Gy and T y , "BP2" for the Blanchard-Perotti approach with
Murchison and Robbins (2003) estimates of Gy and T y , "SR1" for the
sign restrictions approach using Mountford and Uhlig (2005) restrictions,
and "SR2" for the sign restrictions approach that incorporates additional
restrictions. The …gures show the median of the posterior distribution of the
impulse responses as well as the 5% and the 95% fractiles.
4.1
Non-…scal shock
The impulse responses for the non-…scal shock are shown in Figure 3. We see
that the positive hump-shape response of real GDP to the shock is similar
across the di¤erent approaches. Government revenues also exhibit a similar hump-shape response following the non-…scal shock, which re‡ects the
di¤erent automatic stabilizers that compose this variable. The response of
government revenues is almost identical for the two Blanchard-Perotti approaches and the sign restriction speci…cation SR1, whereas it is slightly
weaker for the recursive approach and stronger for SR2. The recursive and
the SR2 approaches would imply respectively output elasticities of government revenues of 1:0 and 2:9. The elasticity of 1:9 estimated by Perotti
(2004) and Murchison and Robbins (2003) is in the middle of these numbers.
Our estimates are also consistent with Kneebone and McKenzie (1997) who
…nd that a one dollar increase in GDP is followed by an increase of 0.28$ of
real net tax revenues.
The response of government expenditures to the non-…scal shock di¤ers
somewhat across the di¤erent approaches. By construction, government ex13
penditures cannot move in the …rst period following the shock for the recursive and the BP1 approaches. This re‡ects the assumption that there are no
automatic stabilizers among the components of government expenditures and
that the government needs at least one quarter to observe and to react to any
shocks a¤ecting the economy. In other words, this is the consequence of the
zero output elasticity of government spending assumption. For these two approaches, government expenditures eventually increase somewhat, although
we cannot reject the no movement assumption given the large con…dence
intervals. At the opposite, BP2 and the two sign restrictions approaches
show that government expenditures decrease immediately after the non-…scal
shock, indicating that the sign restrictions approach supports the Murchison
and Robbin’s (2003) and Kneebone and McKenzie (1997) estimates of the
output elasticity of government spending and reject the calibration used by
Perotti (2004).
4.2
Shock to government revenues
Figure 4 presents the impulse responses to a negative shock on tax revenues.
The impulse responses are quite robust across all the approaches. It takes
about 8 quarters before government revenues return to their initial value.
The shock does not to have any e¤ect on output in the …rst year, except
for SR2 which, by construction, forces GDP to be on positive territory for
the …rst four quarters. Based on the outcome of the other approaches, this
restriction seems to be rejected by the data. A …scal shock that pushes
government revenues down by one dollar is followed about two years later by
an increase of real GDP situated between 0:4 and 0:55 dollar.
The timing and the magnitude of the response of GDP to this shock are
similar to what Perotti (2004) reports for Canada.
As for government expenditures, they do not show signi…cant movements
following this shock. Thus, other components of real GDP (consumption,
investment, and net exports) drive the increase of output following the shock.
4.3
Shock to government expenditures
Figure 5 presents the impulse responses to the government expenditures
shock. The impact of the shock on government expenditures is similar across
all the approaches. It takes about four years before the serie returns to its
14
equilibrium value. However, contrary to the shock to revenues, the impact
on the other variables vary among identi…cation approaches.
With the recursive and the BP1 approaches, a one dollar increase in government expenditures has a very small positive e¤ect on output on impact
(0:5 dollar), and it lasts only one quarter as GDP decrease below its equilibrium value in the second quarter. Perotti (2004) and Phaneuf and Wasmer
(2005), who both use the Blanchard-Perotti approach, also …nd that this
shock has a small and non-persistent e¤ect on Canadian output.
The results with the recursive and the BP1 approaches mean that the
other components of GDP (consumption, investment and net exports) are
signi…cantly decreasing the same quarter than the shock occurs. In fact, after
two quarters, the size of the decrease in the other components of GDP is larger
than the size of the increase in government spending itself. We believe these
strange results re‡ect the fact that these two identi…cation approaches are
unable to isolate a stochastic discretionary …scal spending shock. The shock
we get is probably more a combination of a positive stochastic government
spending shock and a negative non-…scal shock.
To better understand this, remember that …scal policy can be decomposed into three distinct factors: (1) the e¤ect of automatic stabilizers (which
should be nil for government expenditure); (2) the systematic discretionary
response of …scal authorities to business cycles movements; and (3) the stochastic discretionary …scal shocks. In a perfect world, the …rst two factors would entirely be captured by the non-…scal shock, and the government
spending shock would only capture the stochastic discretionary …scal component.
In the data, the ratio of government expenditures to potential output is
negatively correlated to the output gap. Given the absence of automatic
stabilizers for this …scal variable, this probably means that the government
undertook important systematic discretionary countercyclical measures over
history. In section 4.1, we showed that government expenditures are actually
increasing following a positive non-…scal shock if we use the recursive and
the BP1 approaches. This means that these approaches do not allow us
to capture properly the systematic discretionary countercyclical measures
that happened in Canada in response to non-…scal shocks. These systematic
discretionary countercyclical measures are rather captured by the government
spending shock, which means that it is not solely a random discretionary
…scal shock.
At the opposite, the BP2 speci…cation and the two sign restrictions spec15
i…cations yield a larger e¤ect for a government spending shock on real GDP
than the recursive and the BP1 approaches. A one dollar spending shock is
followed by an increase in GDP of one dollar with SR1, 1:4 dollar with BP2
and 1:6 dollar with SR2. GDP remains higher than its equilibrium value for
about three quarters in SR1 and for about four quarters in BP2 and SR2.
The shock has no signi…cant impact on the other components of GDP in
the …rst year following it. They are however strongly decreasing during the
second year.
Finally, no matter the identi…cation approach chosen, the government
spending shock clearly has a smaller e¤ect on the economy after one year
than the shock to government revenues.
4.4
Preferred speci…cation
We prefer the BP2 speci…cation for two reasons. The …rst one is that the BP2
approach yields the most realistic impulse responses. In the case of the government spending shock, it does not generate unrealistic impulse responses
like the recursive and the BP1 approaches. In fact, the impulse responses are
in the same range than the two sign restrictions approaches. For the shock
to net tax revenues, the impulse responses generated by BP2 is similar to
those of the other approaches, except maybe the SR2 approach.
The second reason why we prefer the BP2 approach is that it is the one
that incorporates the less controversial assumptions. For example, it does
not impose restrictions on the initial impact of output following a shock to
net tax revenues like the recursive and the SR2 approaches do. It is true that
the BP2 approach does impose restrictions on the output elasticities of government revenue and expenditure; however, these restrictions are based on
previous empirical work and are in the same range than the elasticities estimated by the two sign restrictions speci…cations. In fact, the sign restriction
approach shows that the output elasticity of government spending of 0:9
assumed in BP2 is supported by the data whereas the 0 elasticity assumed
in BP1 is rejected. The SR1 speci…cation is another approach that do not
incorporate any controversial assumptions. But it does not resist Paustian’s
(2006) criticism since the number of restrictions used to identify the shocks
is too small. In our base case results, this problem does not seem to be too
apparent. But when we use di¤erent sample periods, or when we use di¤erent
approach to detrend the data, the interval of con…dence around the impulse
responses generated by this approach sometimes get extremely wide, high16
lighting the identi…cation problems. When we add extra restrictions (SR2),
we have to impose that GDP must move in the opposite direction than net
tax revenues following a shock to government revenues, which is probably
unrealistic.
4.5
Decomposition of the shocks
To have a better idea about the relative e¤ect of the di¤erent shocks on the
business cycle, we conduct a decomposition of the forecast error variance of
output. We also do it for government expenditures and net tax revenues.
We only describe the results for the BP2 approach, since it is our preferred
approach. The results are presented in Tables 1 to 3.
In the …rst year, most of the ‡uctuations in output are explained by
the non-…scal shock and to a lesser extent, by the government expenditures
shock. The government revenues shock has little e¤ect on output in the …rst
year which is consistent with our results presented in section 4.2. A larger
share of GDP movements in the second and the third years are explained by
this shock, but it remains generally low.
Most of the ‡uctuations of the two …scal variables originate from their
own shock. The non-…scal shock explains up to 40 per cent of the ‡uctuations
in net tax revenues and about 15 per cent of the ‡uctuations in government
expenditures.
Based on the estimated structural innovations and the moving average
representation of the model, it is also possible to measure the cumulated effect of each structural shock on the three variables of the model. In fact, the
sum of the cumulated e¤ect of each structural shock on a variable should be
exactly equal to the historical value of this variable. If we sum together the
e¤ects of the two …scal shocks on a speci…c …scal variable, we can get a cyclically adjusted measure of this …scal variable. Figure 2 shows the cyclically
adjusted series for government expenditures and for net tax revenues (see the
red dashed line). Since most of the short-term ‡uctuations in these series
comes from the structural innovations in the two …scal shocks, we can see
that the cyclically adjusted series follow the actual …scal series very closely.
However, the two recessions in the early 1980s and early 1990s caused important cyclical ‡uctuations in the government net revenues, as well as the
period of strong excess demand in the early 1970s.
17
5
Robustness
5.1
Alternative trends
In the …rst sensitivity analysis, we examine whether changing the trends of
the two …scal variables a¤ects our results or not. In the base case, the series
are detrended with a HP …lter using a lambda parameter of 20 000. We test
three alternative detrending approaches: the linear time-trend, a HP …lter
with a lambda of 1600, and a HP …lter with a lambda of 5000.
It should be noted that when we use a HP …lter with a lambda of 20 000,
the augmented Dickey-Fuller (ADF) test shows that both detrended series are
stationary, although this is true only at the 90% con…dence interval for the
ratio of government expenditures to potential output.6 When the variables
are detrended with a linear time-trend, the ADF test indicates that the
two detrended series still contain unit roots. Finally, when the series are
detrended using a HP …lter with a lambda of 5000 or of 1600, even the
detrended ratio of government expenditures to potential output is stationary
with a con…dence interval of 95%.
Figure 6 compares the impulse responses of our base case VAR with those
obtained with the alternative detrending approaches. We only present the
results for the BP2 approach since we reach the same general conclusions with
the other identi…cation approaches. For the non-…scal shock, we …nd that
the impulse responses of the variables are similar for the di¤erent detrending
approaches and are generally within the con…dence intervals of the base case
estimate. The results are less robust for the two …scal shocks.
In the case of the government revenues shock, the responses of real GDP
and net tax revenues vary greatly between the di¤erent detrending approaches.
When the data are detrended with the linear time-trend, net tax revenues
return very slowly to their equilibrium value and the impact on real GDP is
not signi…cantly di¤erent from 0. At the other extreme, when the data are
detrended with a HP …lter with a lambda coe¢ cient of 1600, the impact on
real GDP is much stronger despite the lower persistence of net tax revenues.
For the government spending shock, the government expenditures are the
only variable that reacts di¤erently across the di¤erent detrending approach.
The linear time-trend is the approach that yields the most persistent re6
For the ADF test, we use the same critical values than for a speci…cation that incorporates both a constant and a time-trend, since we don’t have the exact critical values for
our type of detrending technique.
18
sponses for this variable. When the series are detrended with a HP …lter,
the persistence of this variable decreases gradually with the lambda coe¢ cient. Despite these di¤erences in the persistence of government spending,
the responses of output and net tax revenues to the shock are similar for the
di¤erent detrending approaches.
The purpose of detrending the data is to remove the impacts of permanent
changes in …scal policy. If the impact of temporary and permanent shock was
the same, the method employed to detrend the data would not change the
outcome. Howerver, our results appear to be signi…cantly sensitive to the way
we detrend data. If we had chosen an other method, the previous conclusions
would be di¤erent.
5.2
Subsample stability
With the Blanchard-Perotti approach, Phaneuf and Wasmer (2005) …nd that
the impact of the two …scal shocks on the rest of the economy is not stable
over time in Canada. Perotti (2004) …nd similar evidences for Canada and
other OECD countries. We do a similar robustness exercise by replicating
our experiment over two subsamples.
We set the break point at the last quarter of 1981 as in Phaneuf and
Wasmer (2005). Perotti (2004) used the …rst quarter of 1980. Our conclusions
do not change if we use the same subsamples than Perotti. For the two
speci…cations of the Blanchard-Perotti approach, we use the same output
elasticity of government revenues that Perotti (2004) estimated for the two
sub-sample. In the …rst subsample, it equals 1:61 and for the second one it
equals 2:16.
Figure 7 presents the impulse responses to the three shocks with the BP2
approach for the two subsamples. These impulse responses are compared to
the error bands of our base case results that use the entire sample. Contrary
to Perotti (2004) and to Phaneuf and Wasmer (2005), we …nd, for the shock
to government revenues, that the impulse responses are similar across the
two subsamples and are within the con…dence intervals of the full sample
estimate. This is true for all the identi…cation approaches we tested. This
reinforce our previous conclusion that the results we get for this shock are
quite robust.
The main factor that explains why our results are more stable than those
of Perotti (2004) and Phaneuf and Wasmer (2005) is the way we detrend
the data. To account for the low frequency movements in the data, Perotti
19
(2004) and Phaneuf and Wasmer (2005) incorporate a time-trend in their
VAR speci…cation. As we showed in section 5.1, this detrending method
does not remove all the low frequency movements in the data. Also, the
fact that they incorporate the time-trend directly in the VAR speci…cation
- instead of pre-detrending the series as we do - means that the trend of a
variable in a subsample may be di¤erent than the one estimated over the
entire sample.
The results for the other two shocks are less stable. In the case of the
government spending shock, we can see that the response of government
expenditures is more persistent in the second subsample than in the …rst
one. However, the response of real GDP is relatively constant in the two
subsamples. From these impulse responses, we can indirectly infer that, in
the second subsample, this shock has a pronounce negative impact on the
other components of GDP (consumption, investment and net exports) two
quarters after the shock occurs, whereas in the …rst subsample, the other
components of GDP barely move. This may explain why net tax revenues
increase after the shock in the …rst subsample but decrease in the second one.
The unstable results we get for the shock to government expenditures are
not that surprising given the important changes in …scal policy that occured
in the late 1980s and in the 1990s. To …ght the recurrent large budget de…cit,
the …scal authorities decreased their expenditures dramatically during that
period and it probably modi…ed the link between that variable and the rest of
the economy. Indeed, if we look back at the detrended series for government
expenditures in Figure 1, we see that the persistence of the series increased
dramatically in the second half of the 1980s, which could explain why we
obtain such unstable results.
5.3
Adding additional variables to the VAR
Fatas and Mihov (2001), Perotti (2004), Mountford and Uhlig (2005), Gali
et al. (2007), and Caldara and Kamps (2008) include more variables than
us in their VAR models to evaluate the e¤ect of …scal policy shocks. These
papers include the in‡ation rate and the interest rate among the variables of
their VAR and some of them also incorporate some components of aggregate
demand like consumption and investment or other variables like hours works.
Omitting key variables in a VAR may results in biased impulse responses.
On the other hand, the addition of extra variables increases the uncertainty
around the VAR estimates. It also necessitates the imposition of additional
20
restrictions to identify the shocks, which is not an easy task given the di¢ culty of …nding realistic restrictions.
In this section, we check whether adding more information to the VAR
change the results or not. We add two additional endogenous variables to the
model: the core CPI in‡ation rate7 and the target for the overnight rate. We
also add one exogenous variable, the US output gap, to account for the fact
that Canada is a small open economy. The VAR speci…cation also includes
four lags, based on likelihood ratio tests.
Because we add two endogenous variables, we must identify two new
structural shocks. Since we are adding an in‡ation rate and a short-term
interest rate, we believe we are able to identify a cost-push shock and a
monetary policy shock. In the VAR with three variables, these two shocks
were embedded in the non-…scal shock. To the extent that we view the costpush shock as a type of supply shock, the remaining non-…scal shock in the
VAR with …ve variables can be interpreted as a demand shock.
Of course, the additional restrictions needed to distinguish these two new
shocks from the others di¤er across the di¤erent identi…cation approach. For
example, the papers that use the recursive approach and the BlanchardPerotti approach to identify the structural shocks all impose that the only
variable that is a¤ected contemporaneously by a monetary policy shock is
the interest rate. At the opposite, Mountford and Uhlig (2005), who used
the sign restrictions approach, impose that the in‡ation rate move in the
opposite direction than interest rate after a monetary policy shock for at
least four quarters. A complete description of the restrictions imposed for
each identi…cation approach is presented in Appendix E. It should be noted
that for the two Blanchard-Perotti speci…cations (BP1 and BP2) we use the
price elasticity of government spending and revenues estimated by Perotti
(2004).
Figure 8 compares the impulse responses of the …ve-variables speci…cation
to our base case results. Since the qualitative impact on GDP and on the
two …scal variables of adding extra variables to the VAR is similar across
all the identi…cation approaches for the two …scal shock, we only presents
the results for the BP2 approach. However, the impulse responses for the
cost-push shock and the monetary policy shock di¤er signi…cantly across
7
Core CPI corresponds to the consumer price index excluding eight of the most volatile
components (fruit, vegetables, gasoline, fuel oil, natural gas, mortgage interest, inter-city
transportation and tobacco products) as well as the e¤ect of changes in indirect taxes on
the remaining components. CANSIM identi…er for this series is V41693242.
21
the di¤erent identi…cation approaches. Because the goal of this paper is to
identify …scal policy shocks, we do not present the impact of the other shocks,
but these results are available on demand.
We see that the persistence of real GDP following the demand shock in
the …ve variables VAR is smaller than the one for the non-…scal shock in the
three variables speci…cation. This re‡ects the fact that part of the persistence
of real GDP in the …ve variables VAR is captured by the other two non…scal shocks, in particular the monetary policy shock. As a consequence,
the reaction of net tax revenues is somewhat weaker in the …ve variables
speci…cation than in the three variables one.
In the case of the shock to net tax revenues, the reaction of real GDP and
net tax revenues in the …rst year is similar in the two models. However, in
the second year, the reaction of real GDP in the …ve variables speci…cation
is about half the size than in the three variables speci…cation, even if net tax
revenues take more time to return to their equilibrium value. Even though
the reaction of GDP is smaller in the …ve variables speci…cation, it is still
signi…cantly di¤erent than zero during the second year that follows the shock.
Finally, the impulse responses to the government spending shock of the
…ve variables model are generally within the con…dence bands of the three
variables model. The response of real output to this shock is somewhat
smaller during the …rst year for the …ve variables model, but a similar di¤erence is also observed for government expenditures during the …rst year.
6
Conclusion
Our paper compares the e¤ects of temporary …scal shocks in Canada estimated with di¤erent identi…cation approaches.
Our results show that, following a negative shock to government net revenues, the initial response of GDP is weak, but it increases and reaches a
peak after about two years. All approaches predict similar responses to a
revenues shock and this conclusion is robust across subsamples. However,
when we add variables to the VAR model, the response of GDO is cut by
half.
At the opposite, the response of GDP to the government expenditures
shock are not robust among identi…cation approaches. The RA and BP1 approaches yield an smaller increase than the rise in government expenditures,
while the BP2 and the sign restrictions approches predict a more impor22
tant and persistent impact of the shock. Since the recursive and the basic
Blanchard-Perotti approaches both imply that the output elasticity of expenditures equals zero, though the empirical evidence does not support this
hypothesis (see Murchison and Robbins, 2003), we suspect that the government shock is not correctly identi…ed by these two approaches. We therefore
believe that the responses we obtain with the other approaches are more credible. In addtion, the responses to the shock are not robust across subsample
either. Given the changes in the persistence and the variance of the government expenditures (see Figure 1), it should not be surprising that di¤erent
subsamples yield di¤erent results.
In light of our results, it appears that even if the spending shock has the
biggest e¤ect in the very short run, an unexpected discretionary decrease in
net tax revenues has a more important impact on GDP after a year because
the revenues shock stimulates the components of GDP other than government
expenditures more than the spending shock does.
Our experiments also bring to light the fact that the commonly used
linear time-trend is not an appropriate approach to detrend Canadian …scal
data because it does not eliminate the e¤ects of permanent shocks. We use
a HP …lter to exclude any low frequency movements in the data because we
are primarily interested in the impacts of temporary …scal shocks. When we
use a linear time-trend, the response of GDP to the …scal shocks is weaker
even if the shocks are more persistent. This could mean that the e¤ects of
permanent …scal shocks are di¤erent than those of temporary shocks. We
leave this question for future work.
23
References
[1] Baxter, M. and R. G. King. 1993. "Fiscal Policy in General Equilibrium." The American Economic Review 83(3): 315-34.
[2] Blanchard, O. and R. Perotti. 2002. "An Empirical Characterization of
the Dynamic E¤ects of Changes in Government Spending and Taxes on
Output." The Quarterly Journal of Economics 117(4): 1329-68.
[3] Blöndal, J. R. 2001. "Budgeting in Canada." OECD Journal on Budgeting, 39-65.
[4] Butler, L. 1996. "The Bank of Canada’s New Quarterly Projection
Model, Part 4. A Semi-Structural Method to Estimate Potential Output: Combining Economic Theory with a Time-Series Filter." Bank of
Canada Technical Report No. 77.
[5] Caldara, D. and C. Kamps. 2008. "What are the E¤ects of Fiscal Policy
Shocks? A VAR-based Comparative Analysis." European Central Bank
Working Paper No. 877.
[6] Cayen, J.P. and S. van Norden. 2005. "The reliability of Canadian
output-gap estimates." North American Journal of Economics and Finance 16: 373-93.
[7] Ciccarelli, M. and A. Rebucci. 2003. "Bayesian VARs: A Survey of
the Recent Literature with an Application to the European Monetary
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[8] Fatas, A. and I. Mihov. 2001. "The E¤ects of Fiscal Policy on Consumption and Employment: Theory and Evidence" CEPR Discussion Paper
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[9] Gali, J., J. D. Lopez-Salido, and J. Vallés. 2007. "Understanding the
E¤ects of Government Spending on Consumption." Journal of the European Economic Association 5(1): 227-70.
[10] Kneebone, R. D. and K. J. McKenzie. 1999. "The Characteristics of Fiscal Policy in Canada." Canadian Public Policy - Analyse de Politiques.
XXV(4): 483-501.
24
[11] Mountford, A. and H. Uhlig. 2005. "What are the E¤ects of Fiscal Policy
Shocks?". SFB 649 Discussion Paper No. 2005-039.
[12] Murchison, S. and J. Robbins. 2003. "Fiscal Policy and the Business
Cycle: A New Approach to Identifying the Interaction." Department of
Finance Working Paper 2003-06.
[13] Paustian, M. 2006. "When do sign restrictions work?" Bowling Green
State University Manuscript.
[14] Perotti. R. 2004. "Estimating the e¤ects of …scal policy in OECD countries." IGIER Working Paper No.276.
[15] Phaneuf, L. and É. Wasmer. 2005. "Une étude économétrique de
l’impact des dépenses publiques et des prélèvements …scaux sur l’activité
économique au Québec et au Canada." CIRANO Project Report.
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[17] Sims, C. A. and T. Zha. 1998. "Error Bands for Impulse Reponses."
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25
A
Data
Ratio of gov ernment spending to potential GDP
0.32
Ratio
0.3
Filtered data
Ratio of net taxes to potential GDP
0.35
Ratio
Filtered data
0.3
0.28
0.26
0.25
0.24
0.2
0.22
0.2
1960
1970
1980
1990
2000
2010
1960
Gap of gov ernment spending to potential GDP
0.02
0.04
0.01
0.02
0
0
-0.01
-0.02
-0.02
1960
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
Gap of net taxes to potential GDP
-0.04
1960
1970
1980
1990
2000
2010
Figure 1. Fiscal variables.
Ratio of government spending to potential GDP
0.32
Original serie
Cyc lic ally adjusted serie
Filtered data
0.3
0.28
0.26
0.24
0.22
0.2
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
Ratio of net government revenues to potential GDP
0.35
Original serie
Cyc lic ally adjusted serie
Filtered data
0.3
0.25
0.2
1960
1965
1970
1975
1980
1985
1990
1995
2000
Figure 2. Cyclically adjusted series.
26
2005
2010
B
Decomposition of the shocks
Periods
Non-Fiscal
Tax shock
Spending
shock
shock
1
0:6865
0:0105
0:3030
2
0:7906
0:0103
0:1991
3
0:8272
0:0148
0:1581
4
0:8343
0:0301
0:1355
8
0:7240
0:1547
0:1213
12
0:6362
0:2293
0:1345
Table 1. Decomposition of the shocks for GDP.
Periods
Non-Fiscal
Tax shock
Spending
shock
shock
1
0:1120
0:8742
0:0058
2
0:2457
0:7442
0:0101
3
0:3111
0:6781
0:0108
4
0:3615
0:6256
0:0130
8
0:4389
0:5240
0:0371
12
0:4330
0:5000
0:0670
Table 2. Decomposition of the shocks for government revenues.
Periods
Non-Fiscal
Tax shock
Spending
shock
shock
1
0:1665
0:0026
0:8310
2
0:1579
0:0073
0:8348
3
0:1545
0:0105
0:8350
4
0:1493
0:0141
0:8366
8
0:1317
0:0416
0:8267
12
0:1241
0:0628
0:8132
Table 3. Decomposition of the shocks for government spending.
27
C
10
0
0.5
1
-1
-0.5
0
0.5
1
Periods
0
0
0
Periods
10
Periods
10
Periods
10
BP1
20
20
20
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
-1.5
-1
-0.5
0
0.5
1
1.5
0
0
0
Periods
10
Periods
10
Periods
10
BP2
20
20
20
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
-1.5
-1
-0.5
0
0.5
1
1.5
0
0
0
Periods
10
Periods
10
Periods
10
SR1
20
20
20
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
-1.5
-1
-0.5
0
0.5
1
1.5
Figure 3. Impulse response functions to a non-…scal shock.
-1
20
20
20
-1
10
Periods
10
Periods
-1.5
-1
-0.5
0
0.5
1
1.5
-0.5
0
0
0
RA
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
-1.5
-1
-0.5
0
0.5
1
1.5
Base case results
GDP
Dollars
Net taxes
Dollars
Spending
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
28
0
0
0
Periods
10
Periods
10
Periods
10
SR2
20
20
20
29
GDP
Dollars
Net taxes
Dollars
S pending
Dollars
10
0
0.5
1
-1
-0.5
0
0.5
-1
0
0
0
Periods
10
Periods
10
Periods
10
BP1
20
20
20
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
-1
-0.5
0
0.5
1
0
0
0
Periods
10
Periods
10
Periods
10
BP2
20
20
20
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
-1
-0.5
0
0.5
1
0
0
0
Periods
10
Periods
10
Periods
10
SR1
20
20
20
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
-1
-0.5
0
0.5
1
0
0
0
Figure 4. Impulse reponse functions to a government revenues shock.
Periods
-1
20
20
20
-1
10
Periods
10
Periods
-0.5
0
0.5
1
-0.5
0
0
0
RA
-0.5
0
0.5
1
-1
-0.5
0
0.5
-1
-0.5
0
0.5
1
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Periods
10
Periods
10
Periods
10
SR2
20
20
20
30
0
0.5
1
-2
-1
0
10
0
0
0
Periods
10
Periods
10
Periods
10
BP1
20
20
20
Dollars
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-1
-0.5
0
0.5
1
-2
-1
0
1
2
0
0
0
Periods
10
Periods
10
Periods
10
BP2
20
20
20
Dollars
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-1
-0.5
0
0.5
1
-2
-1
0
1
2
0
0
0
Periods
10
Periods
10
Periods
10
SR1
20
20
20
0
0.5
1
-2
-1
0
1
2
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-1
-0.5
Dollars
0
0
0
Periods
10
Periods
10
Periods
10
SR2
Figure 5. Impulse response functions to a government expenditures shock.
Periods
-0.2
-0.2
0.4
0.6
0.8
1
1.2
-1
-0.5
0
0.5
1
-2
0
20
20
20
0
10
Periods
10
Periods
-1
0
1
0.2
0
0
0
Dollars
0.2
0.4
0.6
0.8
1
1.2
-1
-0.5
GDP
Dollars
Net taxes
Dollars
S pending
Dollars
1
Dollars
Dollars
2
Dollars
Dollars
RA
Dollars
Dollars
2
Dollars
Dollars
20
20
20
D
10
0.4
0.6
0.8
1
-1
-0.5
0
0.5
1
-1
0
5
HP filter (1600)
HP filter (5000)
Time-trend
Base case error bands
Periods
0
0
0
5
5
5
Periods
10
Periods
10
Periods
10
Reponse to tax shock
15
15
15
20
20
20
-0.2
0
0.2
0.4
0.6
0.8
1
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
1.5
0
0
0
Figure 6. Alternative trends (BP2 approach).
-0.2
20
20
20
-0.2
15
15
15
0
10
Periods
10
Periods
0
5
5
-0.5
0
0.5
1
1.5
0.2
0
0
Reponse to non-fiscal shock
0.2
0.4
0.6
0.8
1
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
1.5
Sensitivity analysis
GDP
Dollars
Net taxes
Dollars
Spending
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
31
5
5
5
Periods
10
Periods
10
Periods
10
15
15
15
Reponse to spending shock
20
20
20
0.4
0.6
0.8
1
-1
-0.5
0
0.5
-1
Base case error bands
1982:1 to 2008:2
1961:1 to 1981:4
Periods
0
0
0
5
5
5
Periods
10
Periods
10
Periods
10
15
15
15
Reponse to tax shock
20
20
20
-0.2
0
0.2
0.4
0.6
0.8
1
-1
-0.5
0
0.5
-1
-0.5
0
0.5
1
1.5
0
0
0
5
5
5
Periods
10
Periods
10
Periods
10
15
15
15
Reponse to spending shock
Figure 7. Subsample stability (BP2 approach).
-0.2
20
20
20
-0.2
15
15
15
0
10
Periods
10
Periods
10
0
5
5
5
-0.5
0
0.5
1
1.5
0.2
0
0
0
Reponse to non-fiscal shock
0.2
0.4
0.6
0.8
1
-1
-0.5
0
0.5
-1
-0.5
0
0.5
1
1.5
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
GDP
Dollars
Net taxes
Dollars
Spending
Dollars
32
20
20
20
10
0.4
0.6
0.8
1
-1
-0.5
0
0.5
1
-1.5
Base case error bands
3 variables VAR (base case)
5 variables VAR
Periods
0
0
0
5
5
5
Periods
10
Periods
10
Periods
10
15
15
15
Reponse to tax shock
20
20
20
-0.2
0
0.2
0.4
0.6
0.8
1
-1
-0.5
0
0.5
1
-1.5
-1
-0.5
0
0.5
1
1.5
0
0
0
Figure 8. 5 variables VAR (BP2 approach).
-0.2
20
20
20
-0.2
15
15
15
0
10
Periods
10
Periods
0
5
5
5
-1
-0.5
0
0.5
1
1.5
0.2
0
0
0
Reponse to non-fiscal shock
0.2
0.4
0.6
0.8
1
-1
-0.5
0
0.5
1
-1.5
-1
-0.5
0
0.5
1
1.5
Dollars
Dollars
Dollars
Dollars
Dollars
Dollars
GDP
Dollars
Net taxes
Dollars
Spending
Dollars
33
5
5
5
Periods
10
Periods
10
Periods
10
15
15
15
Reponse to spending shock
20
20
20
E
E.1
Restrictions imposed in the …ve variables
VAR model
2
6
6
6
6
4
E.2
Recursive approach
1
yG
0
1
0
0
1
G
y
TG
Ty
T
rG
ry
r
rT
0
1
0
0
0
0
0
1
0
0
32 3
0 "G
t
6 "yt 7
07
76 7
6 7
07
7 6 "Tt 7
5
0 4 "t 5
1
"rt
0
0
0
1
0
Blanchard-Perotti approach
Under the BP1 speci…cation:
2
1
0
0:12
0
6 yG
1
0
yT
6
6
1
G
y
T
6
4 0
0:43
0:28
1
rG
ry
r
rT
Under the BP2 speci…cation:
2
1
0:21
0:12
0
6 yG
1
0
yT
6
6
1
G
y
T
6
4 0
0:43
0:28
1
rG
E.3
32 3 2
0 uG
1
t
y7
7
6
6
07 6 ut 7 60
6 7 6
07
7 6 uTt 7 = 60
5
0 4ut 5 40
1
urt
0
0
0
0
1
ry
r
rT
32 3 2
0 uG
t
6 uyt 7 6
07
76 7 6
6 7 6
07
7 6 uTt 7 = 6
05 4ut 5 4
urt
1
32 3 2
0 uG
t
6 uyt 7 6
07
76 7 6
6 7 6
07
7 6 uTt 7 = 6
05 4ut 5 4
urt
1
1
0
0
TG
0
1
0
0
TG
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
32 3
0 "G
t
6 "yt 7
07
76 7
6 7
07
7 6 "Tt 7
05 4"t 5
"rt
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
32 3
0 "G
t
6 "yt 7
07
76 7
6 7
07
7 6 "Tt 7
05 4"t 5
1
"rt
Sign restrictions approach
Under the SR1 speci…cation:
2
3 2
Gt
+
6
7
6
yt
6
7 6
6
7 6
t
6
7=6
6
7 60
T
t
6
7 6
4
5 4
rt
(Tt Gt )
0
+ +
+
+
+
+
34
3
2 G3
"
7
+7 6 ty 7
6 "t 7
+7
7 6 "t 7
76 T7
7 4 "t 5
5 r
"t
+
Under the SR2 speci…cation:
2
3 2
Gt
+
6
7
6
yt
6
7 6+
6
7 6+
t
6
7=6
6
7 6
Tt
6
7 6
4
5 4
rt
(Tt Gt )
3
2 G3
0
"
7
+ + + +7 6 ty 7
6 "t 7
+
+ +7
7 6 "t 7
6 7
+
+7
7 4"Tt 5
5 r
+
"t
+
+
35