1. Introduction
In 2008 the Brazilian government, in attempt to unleash more resources to households so as to increase private consumption, widened the existing range of top marginal rates in which the personal income tax was structured. In addition, it lowered the tax on manufactured products (IPI) in the acquisition of cars and trucks. On the spending side, public investment plans as well as government current expenditure growth were maintained throughout the year 2009 in the midst of falling fiscal revenues owing to the economic slowdown (^{MOREIRA, 2010}).
Also, with the aim of boosting aggregate demand, the Brazilian government launched the socalled PAC 2 in March 2010, with an estimate of around R$ 1,59 trillions. This program, which was an extension of the Growth Acceleration Program (Programa de Aceleração do Crescimento  PAC,^{1} in Portuguese) created in January 2007, projected investments of R$ 503,9 billions up until 2010.
This article aims to shed some light on the discussion about the effects of the post2008 Brazilian fiscal policy, on both the revenue and the expenditure sides. Specifically, we set out to examine whether this fiscal expansion had a positive (and permanent) effect on the economic activity by focusing on the analysis of the fiscal multiplier on each sort of stimulus considered, namely tax cuts on consumption, on labor income, on capital gains, government consumption and investment shocks. The baseline model we employ is a small openeconomy New Keynesian one with the standard frictions (price and wage rigidity, habit formation in consumption, investment adjustment costs, Ricardian and nonRicardian consumers, cost of servicing a growing net foreign debt and variable capital utilization) in which both public spending and tax shocks are included and the parameters have been estimated through Bayesian methodology. It also features public capital stock as an input, which allows for the analysis of the effects of shocks to public investment on the marginal productivity of private inputs and on the GDP.
The analyses carried out in this paper highlight that output was mainly driven by changes in the two expenditurebased measures considered, current spending and public investment. From 2003 through 2006, cuts in both expenditure items were instrumental in decreasing aggregate demand. Furthermore, subsequent increases in both items, due to the implementation of PAC1 and, particularly PAC2, were found to be the primary forces behind the renewed impetus to the economic activity and thus, the main lever to overcome the crisis. However, the effects of these expansionary measures only lasted until 2013, when the economy started to deteriorate. Besides, we also find that for the case of Brazil, the fiscal multipliers studied are remarkably low and seem to be in line with the figures that the literature sets for highdebt emerging and developing countries (^{Batini et al., 2014}; ^{Ilzetzki et al., 2013}). As far as the size of the fiscal multiplier is concerned, the most effective stimulus was the consumptiontax cut, followed by the rise in current spending. Incometax related measures and increases in public investment appear to have negligible effects on output. According to our results, the Brazilian government would then be advised to lean on consumptiontax cuts and increases in current expenditure as a way to attain the highest efficacy at boosting output.
The remainder of the paper is organized as follows: section 2 introduces the definition and Literature; section 3 shows the model; sections 4 and 5 explain the data, calibration and estimation of the structural parameters, respectively. Section 6 presents the results; after, section 7 concludes.
2. Fiscal multiplier: definition and literature
This section intends to lay out the fiscal multiplier definition used throughout this paper, as well as present the national and international literature covering the topic at hand.
Definition 2.1 (Fiscal multiplier). It is the ratio of a change in output (ΔY) to an exogenous change in fiscal policy (increase in public spending, (ΔG), or tax cut, (ΔY)). There are different sorts of multipliers:
Impact multiplier =
Multiplier at horizon N =
Cumulative multiplier =
In discussing the values of the multipliers associated with each fiscal policy measure, we choose to work with the latter as it is the most common one used within the literature.
Due to the rapid development of the fiscal policy literature, it is now well accepted that the size of the fiscal multipliers is influenced by several factors. Every time the government carries out an expansionary fiscal policy, a bit of that effect is saved and/or used to buy imports (this is referred to as leakages in the literature). These leakages are greater when it comes to tax exemptions than in the case of public spending, as the latter impacts the aggregate demand directly. That said, some relevant variables that account for the size of those leakages are the marginal propensity to consume, the marginal propensity to import, liquidityconstrained agents (nonRicardian households) and the existence of automatic stabilizers, among others. The way the monetary authority reacts to the fiscal shock is also decisive, as if it accommodates the ensuing demand expansion  by holding the basic interest rate constant in response to this higher aggregate demand , investment and consumption will fall less than in the case the central bank pursues a tighter monetary policy (lower crowdingout effect).
Finally, it can be interesting to present the expected values for the fiscal multipliers. A “rule of thumb” is a publicspending multiplier
The national literature is relatively scant, and this scarcity grows when it comes to articles employing DSGE models to address this issue. However, three articles can be deemed as the pioneers in closing this gap. The first one is ^{Moura (2015)}, where the author uses a DSGE model to derive presentvalue multipliers related to public consumption and investment. Although the aforementioned model has significant strengths, its main weakness has to do with the fact that the author does not consider distortionary taxes into the model, which does not contribute to enriching the debate. His results show that, in spite of the effect of public consumption on GDP being positive on impact, the longrun effect is smaller than unity in all the scenarios analyzed (for some parameterizations the said effect was even negative). According to the author, the cause of this low longrun value resides in the need of fiscal adjustment, leading to future decreases in public consumption and investment. On the contrary, not only does the government investment have a positive impact on the economy in the short run, but its longrun effect exceeds the unity. This is because the bigger stock of public capital brings about productivity gains for the whole economy.
The second paper is ^{Cavalcanti and Vereda (2014)} in which they quantify and compare the macroeconomic impacts of several kinds of public spending  purchases of goods and services, investments, social transfers and public wages and salaries  under different fiscal rules. This work is however limited in the sense that the analysis relies on a calibrated but not estimated DSGE model for the Brazilian economy. The chief results obtained by those authors indicate that, under rules of taxbased fiscal consolidations, the larger positive shortrun effect on GDP arises from the increase in public employment, whereas the most negative effect associates itself with income transfers. On the other hand, under fiscal rules for some spending item, there does not exist any type of public outlay that gives rise to a significant positive impact on GDP in the short run. In the medium run, the best way to make GDP grow is via increases in public investment, which can lead to substantially greaterthanunity multipliers, depending on the fiscal rule in use. In addition, under a permanent balanced budget policy, the majority of public expenditure items yield negligible or even negative multipliers, as opposed to positive ones when a policy of delayed or partial fiscal adjustment is conducted.
^{Carvalho and Valli (2011)} created a model with great acceptance among academics working with DSGE in Brazil. These authors introduced that governments intervene in the economy through the accumulation of public capital with an impact on factor productivity and in the overall demand for investment goods. Different from this work, where the firm does not choose the amount of public capital that one will use in its production process, ^{Carvalho and Valli (2011)} assumed that firms can selectively choose between public and private capital services. This modeling choice was intended to capture the significant presence of the Brazilian government in the productive sector of the economy. This model works with two types of households; the first has more specialized labor services^{2} where the second does not. Wages and prices have rigidities but there are still consumption habits. Among the shocks proposed by the authors, there are shocks in the primary surplus/GDP, in the public investments and in public transfers/GDP.
In the international literature, DSGE models are relied upon even more intensely in the study of fiscal multipliers. ^{Zubairy (2010)} estimates a DSGE model with fiscal features using Bayesian techniques for the U.S. economy. The author finds a publicspending multiplier of 1,12, in contrast to the tax exemptions from labor income and capital income, whose multipliers are 0,13 and 0,33, respectively. ^{Christiano et al. (2009)}, by means of a DSGE model, seek to obtain a greaterthanone multiplier when the economy is at the zero lower bound. They come up with a multiplier effect which is substantially larger than one, this result being fully consistent with the behavior of the main macroeconomic variables over the 2008 crisis. ^{Woodford (2010)} also tackles shocks to government expenditures. Throughout this article, the author aims at providing an explanation for the main factors determining the efficiency of fiscal stimulus on output and employment by using a NewKeynesian model. Results show that delays in the price and wage adjustment can raise the size of publicspending multipliers, and that its value would be bigger than one as long as the monetary authority keeps interest rates unchanged. Meanwhile, that value can be far lower if the monetary authority bids up interest rates in response to a rise in spending.
It may also be worth reviewing some articles that do not resort to DSGE models in accounting for the effectiveness of fiscal policies and their associated multipliers for the case of Brazil. ^{Cavalcanti and Silva (2010)} attempt to understand the effects of fiscal policy for this economy over a period spanning 1995 to 2008 by making use of a VAR model that emphasizes the role of public debt in the efficiency of fiscal policy. Their results suggest that there exists an explicit role of public debt in the evolution of the fiscal variables over economic activity. Therefore, a fiscal shock influencing public debt should engender future movements in public expenditures and revenues which tend to attenuate the initial effects of the shock.
^{Mendonça et al. (2010)} deploy data spanning from 1995 to 2007, so as to investigate the effects of fiscal shocks on the Brazilian economy. Their results imply that private consumption and interest rates rise as government spending unexpectedly goes up. Nevertheless, output is very likely to fall. These results point to the presence of crowdingout effects between public spending and private investment. As regards the expansionary shock to revenues, it is possible for output to drop in the short run, but a positive reaction of this variable is likely to materialize in the longer run.
^{Peres and Ellery Junior (2009)} examine the dynamic effects of shocks to federal fiscal variables on the economic activity in Brazil for the postRealPlan period by utilizing a Structural VAR comprising output, public spending and net taxes. These authors compare their results with those found in the international literature for the case of the American economy and other OCDE countries and come to the conclusion that they are similar in that the output response to fiscal shocks is positive but small in both economic areas.
^{Fantinatti (2015)} looks into the policy of tax exemption applied to the IPI on durable goods during the postcrisis 2008 period. His results underline the fact that fiscal boosts in the sector of durable goods were unimportant, and apparently the best taxexemption policy would be to foster the sector of nondurable goods on account of two main reasons: the share of nondurable goods over GDP; and the assumption that government consumption is biased towards nondurable goods, which renders fiscal adjustment less imperative.
3. The model
Our model follows the NewKeynesian tradition and, in addition to price frictions, it features wage rigidity. It also encompasses nonRicardian agents, habit formation in consumption, investment adjustment cost, cost of servicing a growing net foreign debt, and variable capital utilization. This section intends to describe the economy under discussion by focusing first on households, then presenting firms, next the government and ending with the external sector.
3.1. Households
There is a continuum of households indexed by j ∈ [0,1]. A share ω_{R} of this continuum of households indexed by R ∈ [0,ω_{R}) have access to financial markets, and they behave as Ricardian agents, that is, they maximize their intertemporal utility. The remaining share of households indexed by NR ∈ (ω_{R},1] cannot save and simply consume their aftertax disposable income. This type of agent is referred to as nonRicardian household in the literature.
3.1.1. Determining consumption and saving of the Ricardian household
The representative ricardian household is assumed to maximize its intertemporal utility by choosing consumption, savings, investment and leisure. As for the saving decision, she can choose between three different instruments  physical capital, foreign bonds and government bonds, indexed by j. In other words, this agent elects how much to consume, how much to work and how much to save and invest by accumulating financial assets and physical capital in order to maximize the discounted stream of expected utility.
The standin consumer’s formal problem boils down to,
subject to her budget constraint,
and to the following law of motion for capital,
The intertemporal preference shock:
where ε_{P,t} ~ N(0,σ^{P}).
The labor supply shock:
where ε_{L,t} ~ N(0,σ^{L}).
The quality of investment shock:
where ε_{I,t} ~ N(0,σ^{I}).
where E_{t} is the expectations operator, 0 < β < 1 is the intertemporal discount factor, C_{R} denotes consumption, L_{R} denotes labor, S^{P} refers to the intertemporal shock, S^{L} is the shock on labor supply, φ is the marginal disutility of labor and σ is the coefficient of relative risk aversion.
Regarding the budget constraint, P is the general price level, I^{P} is private investment, B is a oneyear government bond, B_{F} is a oneyear foreign bond, R_{B} is the rate of return on the government bond (basic interest rate), R_{F} denotes the world interest rate, S is the nominal exchange rate, W is the wage, R is the return to capital, K^{P} is the private stock of capital, U is the capital utilization rate, χ is a parameter governing the adjustment cost’s sensitivity, TRANS is the net income transfers to households by the government, τ^{C}, τ^{L}, τ^{K} stand for the consumption tax rate, laborincome tax rate and capitalincome tax rate, respectively. The term
We adopt the convention that B and B^{F} are the nominal bonds issued in (t1) and matured in t. For convenience, all bonds are regarded to be oneperiod bonds. Hence, both B_{t+1}, B_{t+1}^{F} and K_{t+1}^{P} are decided in t.
Solving the Ricardian household’s problem, we are left with the following firstorder conditions:
3.1.2. Determining consumption and saving of the nonRicardian household
The nonRicardian household’s behavior is simpler owing to her liquidity constraint which does not enable her to maximize her utility intertemporally. Thus, the nonRicardian agent’s consumption must match her current income each period. In reality, even without access to “credit”, this kind of agent would be able to carry over current income into the future (by saving). In order to make the model more tractable, this agent will be also assumed to be unable to save. Therefore, the problem faced by this nonRicardian consumer is:
subject to her budget constraint,
The firstorder condition is the following:
3.1.3. Wage setting
The household’s choice over the wage level entails the assumption that this agent supplies differentiated labor under a monopolistically competitive framework. This service is sold to a representative labor aggregator which combines all those different labor services (L_{J}) into a single input (L) by means of the DixitStiglitz technology.
subject to the following technology:
The firstorder condition is given by:
This equation represents the household j’s demand for labor. Plugging the latter into the preceding technology (17) results in the aggregate wage level:
In each period, a share 1θ_{W} of households, which are randomly and independently chosen, set their wage in an optimal manner. The remaining households, θ_{W}, follow a stickywage rule (W_{j,t} = W_{j,t1}).
In taking the decision to pick their wage level in the period t, the wagesetting households are aware they face the probability θ_{W}^{N} of the wage being fixed for N periods in the future, regardless of whether the household makes the optimal choice W_{j,t}^{*} in the current period. Accordingly, the household seeks to solve the following problem:
where Z = {R, NR}.
subject to the household j’s demand for labor (18).
Solving that problem yields the following firstorder conditions for both the Ricardian and nonRicardian households:
Because a share 1θ_{W} of the households elect the same nominal wage, W^{*}_{J,t}, and the remaining share, θ_{W}, receive the same wage as in the preceding period, the aggregate nominal wage can be written as follows:
The gross wageinflation rate can be defined as:
3.2. Firms
3.2.1. Final good producer (Retail)
From an aggregate perspective, monopolistic competition involves, among other things, confronting the fact that consumers purchase a great variety of goods with the need of modeling in which the consumer is assumed to buy only a specific kind of good (a bundle comprised of all goods). This aggregate good is sold by a perfectly competitive retail firm. In other words, all the retailers are assumed identical to each other.
With the target of producing a bundle, the retailer must buy a large amount of wholesale goods. These are the inputs used in its production process. Thus, the retail firm acquires a great variety of wholesale goods (clothing, electronics, etc.) and bundles them into a final good (a basket of goods) which will be sold to the final consumer. In order to pose the problem faced by the retailer and solve for it, we must first describe its production technology. The aggregation technology is given by the DixitStiglitz aggregator (^{DIXIT and STIGLITZ, 1977}).
where Y_{t} is the retailers’ output over periods t, and Y_{j,t} for j ∈ [0,1] is the wholesale good j. Ψ > 1 refers to the elasticity of substitution between wholesale goods.
It should be noted that the price of each wholesale good is taken as given by the retailer. Knowing that P_{t} and P_{j,t} denote the nominal prices of the retail good and the wholesale good j, respectively, the representative retail firm’s maximization problem takes the form:
Substituting the aggregator (27) into the last Equation (28) leads to the following expression:
By taking the firstorder condition of the above problem, we get:
This function portrays the demand for the wholesale good j, which rises with aggregate demand and is inversely related to its relative price level.
Plugging Equation (30) into Equation (27) yields the aggregate price level:
3.2.2. Intermediate good producer (wholesale)
Taking into account that domestic output is given by Y = {C, I^{P}, G, X}, an intermediategood producing firm solves its problem in three steps: First, it chooses labor and capital so as to produce domestic inputs; right after, in order to determine the level of its output, it chooses between domestic inputs versus imported inputs; finally, it sets the price of the good it sells.
In the first step, the firm operates under perfect competition and produces a domestic input, INP^{D}_{j,t}, using the following technology:
where α_{1}, α_{2} and α_{3} stand for the share of private capital, labor and public capital in the production of domestic inputs, A captures the economy’s level of technology which obeys the following law of motion:
where ε_{A,t} ~ N(0,σ^{A}).
Hence, the firm’s goal is to minimize the cost of production:
subject to the prior technological restriction (31).
It is not difficult to show that the firstorder conditions with respect to K^{P}_{j,t} and L_{j,t} are:
The marginal cost is given by:
In the second step, as already mentioned, the firm engages in decisionmaking regarding the choice between using domestic inputs versus imported ones by means of the following technology:
where ω_{D} represents the share of the domestic input in the production of the intermediate good, and Ψ_{D} is the elasticity of substitution between domestic inputs and imported ones.
So the firm’s problem at this stage can be formally stated as:
subject to the above technology.
By solving the previous problem, we obtain the following firstorder condition:
and,
And the marginal cost is:
3.2.3. Pricing a la Calvo
The third step of this problem amounts to setting the price of its good. This wholesale firm decides how much to produce in every period according to the Calvo rule (^{CALVO, 1983}). There is a probability θ that the firm keeps the price of the good fixed in the next period (P_{j,t} = P_{j,t1}) and a probability (1θ) that it sets the price optimally (P^{*}_{j,t}). Once the price has been set in period t, there is the probability θ that this price will remain fixed in period t+1, a probability θ^{2} that this price will remain fixed in period t+2, and so on. Accordingly, this firm should take into account these probabilities when setting the price of its own good. The problem of the firm that adjusts the price of the good in period t is:
subject to the demand for good Y_{j,t+i}(30).
The following firstorder condition is obtained by rearranging further the preceding equation:
It is worth noting that all wholesale firms setting their prices share the same markup over the same marginal cost. This means that in all periods P^{*}_{j,t} the price is the same for all (1θ) firms adjusting their prices. Combining now the pricing rule (31) with the assumption that all pricechanging firms set an equal price and that pricemaintaining firms leave the price unaffected  since they share the same technology , yields the overall final price:
3.3. Government
In our model the government comes into the picture by splitting itself into two different entities: a fiscal authority and a monetary authority. The former is held responsible for conducting fiscal policy, while the latter pursues the price stability through a Taylor rule.
3.3.1. Fiscal authority
The fiscal authority is tasked with taxing households’ income and issuing debt to finance its outlays, namely: current expenditure, G_{t}; public investment, I_{t}^{P}; and net transfers to households, TRANS_{t}. So the government’s budget constraint can be represented by:
The overall tax collection would be:
The fiscal authority has three expenditurebased fiscal policy tools at its disposal: G_{t}; I_{t}^{P}; and TRANS_{t}. On the revenue side, the tools the fiscal authority falls back on are: τ_{t}^{C}; τ_{t}^{L}; and τ_{t}^{K}. All these instruments follow the same fiscal policy rule:
where γ_{Z} and ϕ_{Z} are parameters capturing the importance of these fiscal policy tools relative to public debt sustainability, and the importance of the rule debt level relative to GDP, respectively, and Z = {G_{t}, I_{t}^{G}, TRANS_{t}, τ_{t}^{C}, τ_{t}^{L}, τ_{t}^{K}}.
The fiscal shock can be expressed as:
where ε_{Z,t} ~ N(0,σ^{Z}).
Likewise, the stock of public capital evolves according to the well known law of motion:
where δ_{G} denotes the rate of depreciation of public capital.
3.3.2. Monetary authority
The Central Bank’s task is twofold: to foster output growth and to attain price stability. In order to accomplish this dual goal, it pursues a simple Taylor rule:
where γ_{Y} and γ_{π} are the sensibilities of the interest rate to output and to the inflation rate, respectively, and γ_{R} is a stabilization parameter. S_{t}^{m} is the monetary shock, which abides by the following expression:
where ε_{m,t} ~ N(0,σ^{m}).
3.4. External sector
The external sector is represented by the demand for the exported good, by the equilibrium condition of the balance of payments, and by the law of motion governing the movement of the foreign interest rate and the import price level. The export demand obeys a rule which depends on a stabilization component, on the real exchange rate and on a stochastic component:
where γ_{X} is a stabilization parameter, ϕ_{X} is the sensibility of exports to the real exchange rate and S_{t}^{X} is the shock to export demand, which is given by:
where ε_{X,t} ~ N(0,σ^{X}).
The externalsector balanced condition (balance of payments) can be stated as:
The laws of motion for foreign interest rates and import price level are defined as:
where ε_{RF,t} ~ N(0,σ^{RF}).
where ε_{PF,t} ~ N(0,σ^{PF}).
4. Data
We then proceed to estimate the model using quarterly data spanning from 2002Q1 to 2014Q4 (52 data points). We use 14 model variables as observables (P, TRANS, RTL, RTKp, RTC,^{3}R_{B}, Y, C, G, C, X, IMP, R^{F}, S, L) which they are described in the Table 1. So, to prepare the data for the model estimation, we deflated using the IPCA, detrented and seasonally adjusted non stationary series using the software X12ARIMA and applied first logdifference. We have chosen this set of observables due to data availability and their relevance to our research purposes. Furthermore, a large set of observables mitigates the problem of identification.
Variable  Series  Source 

P  Series constructed using the IPCA (\%a.m.)  IBGE/SNIPC 
TRANS  Benefícios assistenciais (LOAS e RMV) R\$ (milhões)}  Min. Fazenda/STN 
RTL  IR  pessoas físicas R\$ (milhões)  Min. Fazenda/SRF 
RTKp  IR  pessoas jurídicas R\$ (milhões)  Min. Fazenda/SRF 
RTC  ICMS and IPI R\$ (milhões)  Min. Fazenda/SRF 
R^{B}  Selic Over (\% a.m.)  BCB Boletim/M. Finan. 
Y  PIB  preço de mercado  R\$ (milhões)  IBGE/SCN 2000 Trim. 
G  Consumo final  adm. pública  R\$ (milhões)  IBGE/SCN 2000 Trim. 
C  Consumo final  famílias  R\$ (milhões)  IBGE/SCN 2000 Trim. 
X  Exportações  R\$ (milhões)  IBGE/SCN 2000 Trim. 
IMP  Importações  R\$ (milhões)  IBGE/SCN 2000 Trim. 
L  Horas pagas  indústria geral  índice (jan. 2001 = 100)  PIMES/IBGE 
R^{F}  Estados Unidos  taxa de juros (\% a.a.)  Fundo Monetário Internacional, International Financial Statistics 
S  Taxa de câmbio  R\$ / US\$  comercial  compra  média  Banco Central do Brasil, Boletim, Seção Balanço de Pagamentos (BCB Boletim/BP) 
Source: Own calculations.
5. Calibrated parameters, prior and posterior
In this section we pursue a twotier approach: the parameters not directly related to the questions which we endeavor to answer throughout this article are calibrated, while those relevant parameters for the analysis of the shock propagation are estimated using the Bayesian methodology. The main calibration procedure employed here is to pick up the values of parameters from other relevant articles in the DSGE model literature. Table 2 summarizes the calibration of the parameters.
Parameters  Value  Source 

β  0.985  Cavalcanti and Vereda (2010) 
σ  2  Cavalcanti and Vereda (2010) 
σ  1.5  Cavalcanti and Vereda (2010) 
α_{1}  0.3  Mussolini (2011) 
α_{2}  0.6  Mussolini (2011) 
α_{3}  0.1  Mussolini (2011) 
δ  0,025  Cavalcanti and Vereda (2010) 
δ_{G}  0.025  Cavalcanti and Vereda (2010) 
ω_{R}  0.6  Castro et al (2011) 

0,1  Sensitivity Analysis (Iskrev, 2010) 

1  Sensitivity Analysis (Iskrev, 2010) 

0,1  Sensitivity Analysis (Iskrev, 2010) 
ψ_{2}  1  Sensitivity Analysis (Iskrev, 2010) 
χ  1  Sensitivity Analysis (Iskrev, 2010) 
γ_{G}  0  Stähler and Thomas (2012) 
ϕ_{G}  0  Stähler and Thomas (2012) 
γ_{1G}  0  Stähler and Thomas (2012) 
ϕ_{1G}  0  Stähler and Thomas (2012) 
ψ 

Predetermined 
Source: Own calculations.
^{Iskrev (2010)} provides a method for testing the set of combination of parameters’ values in order that ^{Blanchard and Kahn (1980)} conditions are met. Subsequently, from this set of values the procedure was to choose those values for the parameters that fulfill the conditions which are considered standard in the literature. As in 2014 the public sector net external debt was around 10% of GDP, the parameter
Obtaining the average value of total transfers from the government to households is by no means an easy task. This is why we reckon that a value of 10% as a percentage of GDP would be more than acceptable
The parameters γ_{G}, ϕ_{G}, ϕ_{IG} and γ_{IG} were set at zero, following ^{Stahler and Thomas (2012)}. This choice implies that fiscal policy reacts through changes in taxes, and not through changes in government spending. This seems to be the case in key episodes of recent Brazilian economic history. For instance, at the outset of the Real plan, the fiscal consolidation process mainly rested on the CPMF (Temporary Tax on Financial Transactions, Contribuição Provisória sobre Movimentação Financeira in Portuguese).^{4} Given the prior distributions of the parameters, we estimate the posterior distributions using a Markov chain process via the MetropolisHastings algorithm with 100.000 iterations, a scale value 0.3 to be used for the jumping distribution, and 10 parallel chains for MetropolisHastings algorithm.^{5} The results of the Bayesian estimation are shown in Table 3 and Figure 1.
Parameter  prior mean  post. mean  90\% HPD interval  prior  pstdev 


0.160  0.1640  0.1519 0.1760  beta  0.0100 

0.170  0.1772  0.1694 0.1855  beta  0.0100 

0.080  0.0616  0.0528 0.0702  beta  0.0100 
γTRANS  0.500  0.5614  0.4560 0.6900  beta  0.1000 
γ_{τC}  0.500  0.7303  0.6409 0.8369  beta  0.1000 
γ_{τL}  0.500  0.5166  0.4244 0.6037  beta  0.1000 
γ_{τK}  0.500  0.4959  0.3764 0.6131  beta  0.1000 
ϕ_{TRANS}  0.500  0.2750  0.5127 0.0897  unif  0.2887 
ϕ_{τC}  0.500  0.5632  0.2802 1.0000  unif  0.2887 
ϕ_{τL}  0.500  0.0163  0.0000 0.0404  unif  0.2887 
ϕ_{τK}  0.500  0.0374  0.0000 0.0794  unif  0.2887 
χ _{BF}  0.003  0.0045  0.0050 0.0039  unif  0.0014 
γ _{X}  0.500  0.5042  0.3953 0.6010  beta  0.1000 
ϕ _{X}  0.500  0.1456  0.0000 0.3211  unif  0.2887 
ω_{D}  0.850  0.8364  0.8240 0.8493  beta  0.0100 
ψ_{D}  5.000  3.2352  2.8044 3.6456  gamma  0.5000 
ϕ_{INSD}  0.850  0.8787  0.8280 0.9330  beta  0.0500 
θ  0.750  0.7445  0.7285 0.7587  beta  0.0100 
θ_{W}  0.750  0.7535  0.7443 0.7638  beta  0.0100 
ψ  10.000  13.0704  8.7269 18.4005  gamma  5.0000 
ψ_{W}  10.000  15.4805  9.2004 27.2836  gamma  5.0000 
ϕ_{C}  0.800  0.7957  0.7850 0.8052  beta  0.0100 
γ_{R}  0.500  0.3262  0.2338 0.4251  beta  0.1000 
γ_{Y}  0.500  0.4530  0.3985 0.5070  gamma  0.0500 
γ_{π}  3.000  3.0646  2.9539 3.1823  gamma  0.1000 
ρ_{a}  0.500  0.5549  0.4837 0.6312  beta  0.1000 
ρ_{G}  0.500  0.4751  0.3675 0.5866  beta  0.1000 
ρ_{IG}  0.500  0.5187  0.4288 0.6076  beta  0.1000 
ρ_{TRANS}  0.500  0.5713  0.4729 0.6780  beta  0.1000 
ρ_{τC}  0.500  0.5450  0.4274 0.6552  beta  0.1000 
ρ_{τL}  0.500  0.3698  0.2677 0.4684  beta  0.1000 
ρ_{τK}  0.500  0.6862  0.5464 0.8346  beta  0.1000 
ρ_{m}  0.500  0.5450  0.3892 0.7256  beta  0.1000 
ρ_{P}  0.500  0.4334  0.3665 0.5150  beta  0.1000 
ρ_{L}  0.500  0.4571  0.3523 0.5652  beta  0.1000 
ρ_{I}  0.500  0.6123  0.5276 0.7025  beta  0.1000 
ρ_{X}  0.500  0.4939  0.3838 0.6053  beta  0.1000 
ρ_{RF}  0.500  0.5828  0.4928 0.6684  beta  0.1000 
ρ_{PF}  0.500  0.7764  0.6953 0.9045  beta  0.1000 
ε  1.0  0.1321  0.1176 0.1476  invg  Inf 
ε_{G}  1.0  0.1308  0.1176 0.1452  invg  Inf 
ε_{IG}  1.0  1.3021  0.9808 1.7152  invg  Inf 
ε_{TRANS}  1.0  0.5577  0.2982 0.7773  invg  Inf 
ε_{τC}  1.0  0.2236  0.1620 0.2732  invg  Inf 
ε_{τL}  1.0  0.1827  0.1504 0.2129  invg  Inf 
ε_{τK}  1.0  0.2195  0.1798 0.2587  invg  Inf 
ε_{m}  1.0  0.1272  0.1176 0.1383  invg  Inf 
ε_{P}  1.0  0.3266  0.1955 0.4582  invg  Inf 
ε_{L}  1.0  0.4286  0.2229 0.6244  invg  Inf 
ε_{I}  1.0  0.5671  0.4055 0.7249  invg  Inf 
ε_{X}  1.0  0.1386  0.1176 0.1561  invg  Inf 
ε_{RF}  1.0  0.1267  0.1176 0.1377  invg  Inf 
ε_{PF}  1.0  0.1468  0.1214 0.1691  invg  Inf 
Source: Own elaboration.
These graphs are especially relevant in that they present key results, but they can also serve as tools to detect problems or build additional confidence in one’s results. First, the prior and the posterior distribution should not be excessively different from one another. Second, the posterior distributions should be close to normal, or at least not display a shape that is clearly nonnormal. Third, the green mode should not be too far away from the mode of the posterior distribution. Overall, it is worth pointing out that the estimates proved to be quite satisfactory.
6. Results
This section analyzes the dynamic properties of the model by focusing on the shocks decomposition of the GDP and the fiscal multipliers.
6.1. Shocks decomposition
One way to assess the effects of the different shocks on GDP fluctuations is to look into the decomposition of these shocks (Figure 2). Two variables were found relevant in accounting for the output behavior: current spending and public investment. Both performed similarly, reducing output over the period 2003 to 2006, as a strong fiscal adjustment was under way. However, during the period in which the Growth Acceleration Programs (PAC, in Portuguese) prevailed  PAC1 and PAC2 were initiated in 2007 and 2010, respectively , government expenditure and public investment played an important role in boosting aggregate demand.
In this section, we turn to gauging the fiscal multipliers for each fiscal shock (Figure 3). The results are in accordance with what was presented in Section 2, namely, in the smalleconomy case the multipliers should be smaller than 0.5  it is worth remarking that these would be even smaller if there were a pressing need to put the fiscal house in order to keep public debt stable (^{Spilimbergo et al., 2009}). The greatest multiplier found in this work was that of the consumptiontax excise reduction. Its associated value was 0.09 on impact, reaching 0.12 at 8 periods, with this number falling steadily over 16 quarters on the grounds of the need to adjust other fiscal tools, since the falling tax revenues led to a growing public debt (perceived effect by ^{MOURA (2015)} and by ^{CAVALCANTI and SILVA (2010)}). This growth was, however, temporary and the multiplier resumed growing.
The secondlargest multiplier is the one associated with public spending. On impact, its value was 0.055. The ensuing fiscal adjustment caused this value to drop (for the same reason as in the case of the preceding multiplier), bottoming out at 0.04 and then bouncing back thereafter until reaching a stable level. Concerning the publicinvestment multiplier, its value on impact was smaller than the earlier figures, 0.003, it thereon embarked on a downward path (thereby mimicking somehow the behavior of the prior fiscal measures’ multipliers) but its upward trajectory after the rebounding was steeper than those of the previous fiscal policies. The reason is that a positive shock to public investment renders firms more productive as the higher investment turns into capital stock (In the same way as in ^{MOURA (2015)}).
The only incometax measure yielding a positive multiplier is the tax exemption from labor income. On impact, the value was modest  0.005 , but in the longer run this number improved due to the increase in the households’ labor supply. The same policy applied to capital income gave rise to a negative result at any horizon.
7. Conclusions
This article intended to make a contribution to the discussion about the effects of the Brazilian fiscal policy after the 2008 crisis. In this vein, a shocks decomposition for Brazilian GDP as well as a multiplier analysis of each fiscal shock were undertaken under the framework of a New Keynesian model. The spendingbased measures were the most successful in affecting GDP over the whole period studied, primarily because of PAC2, whose actual goal was to bolster aggregate demand. However, this stimulus program had a positive result until 2013, thereafter the deterioration of this type of fiscal policy negatively affected the Brazilian economic result.
The form chosen to compare the different possibilities of fiscal policies was the fiscal multiplier. The exemption of tax on consumption showed better results, followed by the multiplier of public spending. The other multipliers showed relatively insignificant. Given these results, relieve the tax on consumption and increase current spending would be the best possibilities to stimulate the economy. Still, it can be noted in the shocks decomposition, that this second policy was one of the tools used to stimulate the economy in the PAC programs.