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The present study measured the effectiveness of Brazilian fiscal policy (the effects of fiscal shocks on output) through several specifications of SVAR models. The focus was on the impact of tax shocks on output, but spending shocks effects were also estimated. Two databases for fiscal variables were used: the official data from National Treasury and a set of alternative data by Gobetti and Orair [1] . The tax multiplier depends on the assumption about the sensitivity of government’s revenue to output: the greater the sensitivity, the greater is the tax multiplier. The preferred estimates of tax multipliers in this paper are higher than other estimates in the Brazilian literature. In most identifications both spending and tax (impact) multipliers are below unit.

According to the empirical literature on fiscal policy, fiscal multipliers tend to vary between countries and even within the same country over time. The magnitudes of the multipliers are influenced by various macroeconomic conditions and even the strategy of empirical estimation. Among the idiosyncrasies that can affect the extent of fiscal impacts there are the following: the economy openness to external markets, its exchange regime and stage of economic development [^{1} the phase of the economic cycle [^{2} Most of the empirical literature uses time series methodology to measure the impact of fiscal policy.

In Brazil, fiscal policy empirical literature related to vector autoregressive models (VAR) suggests the existence of “Keynesian” fiscal multipliers,^{3} especially in relation to the macroeconomic effects of government spending. Notwithstanding, there are some literature suggesting the possibility of unconventional effects: fiscal multipliers close to zero and even cases in which output responds negatively (positively) to positive spending (tax) shocks.^{4} Most of the empirical studies on fiscal policy in Brazil also use autoregressive models with structural identification approach (SVAR), even though there are more sophisticated studies (e.g., Bayesian, Markovian regime change, etc.). The present study uses the SVAR most common identification procedure, applying it to two different samples of fiscal data.

In respect to tax shocks, Brazilian literature finds that these tend to be less effective than spending shocks. Reviewing the relevant literature, one will find it is more common to find insignificant responses to tax shocks than to spending shocks, even though, as mentioned, that doesn’t mean that spending shocks are always significant. One can find low fiscal effects in both instruments in Mendonça et al. [^{5} Peres and Ellery Jr. [

This study tests the effects of tax shocks on output, vis-à-vis the effects of spending shocks in the Brazilian economy—given the apparent evidence of a lower effectiveness of the tax shocks mentioned in the previous paragraph—from a structural autoregressive model. The question to be answered in this study is the following: given the data generation process (DGP) established by the VAR model, under which conditions can a tax shock generate a stronger (or weaker) response of GDP? Or, in other words, under which conditions one can generate a high tax multiplier? This question is answered through a sensitivity analysis on one key-parameter of the structural identification procedure: the income-elasticity of tax revenues. The process of identifying the structural model follows BP [

The procedure of empirically estimating SVAR models implies, at first, estimating the models in a reduced form, which establishes the data generation process for the model’s endogenous variables in terms of the past values of its own variables. The model in its reduced form is compatible with various forms of identification. In turn, each identification can be used to access different dynamic responses of the system to shocks. As will be seen in the methodological section, a reduced-form autoregressive model is not appropriate for economic analysis due to correlations between the equations’ errors (one cannot conduct a true ceteris paribus analysis). The structural approach imposes a set of contemporaneous correlations between the endogenous variables that becomes an integral part of the empirical model and, if successful, makes all contemporaneous correlations explicit, transforming the errors into white-noise processes.

In terms of choosing contemporary relationships, the Cholesky decomposition—used in various empirical works cited above—imposes a specific ordering on these contemporaneous relationships between endogenous variables, preferably in accordance with economic rationality. In most cases, the SVAR approach can be summarized as a “zeroing” procedure, that is, assuming that some contemporaneous correlations are equal to zero to the point that the system can be exactly identified. BP [^{6} Adding other reasonable assumptions about the delay or rigidity government spending, identification of the three-variable model was possible. BP’s seminal methodology has been adapted to the Brazilian economy by Peres and Ellery Jr. [^{7} but focusing on spending multipliers.

The sensitivity analysis on the income-elasticity of tax revenues reveals, in this study, that there is a positive relationship between this parameter and the tax-elasticity o output^{8} (the instantaneous response of output to variation in government tax revenues): when its assumed a high sensitivity of tax revenues to output, the result matrix of contemporaneous relationships will be such that taxes will have a great and immediate impact on GDP. These relationships will be passed on to the estimated impulse-response functions and, finally, to multipliers. The estimates of the study suggest that tax shocks cause output responses that are statistically significant when income-elasticity in relatively high, that is, equal or above 2%.^{9} When the elasticity is exactly equal to 2% the impact tax multiplier can reach −$0.53; when the elasticity is supposed to be between 2.5 and 3 the estimated multiplier rises (in magnitude) to −$0.81 and −$1.1, respectively. At the same time, the impact multipliers of government spending were estimated between $0.61 and $0.71, depending on the fiscal data used. The accumulated response to fiscal policy can be even stronger: when the income-elasticity to tax is 2.5, the accumulated tax multiplier after ten quarters can reach the maximum of −$1.83, while the accumulated spending multiplier, for the same horizon, $1.33.

The description of the multipliers in intervals in the last paragraph is due to the fact that this study uses two distinct fiscal databases. The first database is the official series of the central government, from the National Treasury. The second database is an alternative, non-official, government series produced by the federal government’s economic research institute (Ipea). Ipea’s alternative series are described by Gobetti and Orair [

The rest of this article is organized as follow: the next section describes the identification methodology—from the reduced-form VAR model to the structural model. Section 3 describes the two sets of fiscal data available: the fiscal variables from the National Treasury and the alternative database produced by Gobetti and Orair [

This section presents the structural identification methodology for the VAR models. The following exposition assumes the auto-regressive description of a stationary data generating process. Stationarity and stability result in parameters whose estimations have desirable properties, such as well-behaved impulse-response functions, with variances that are not explosive over the long term. Complete details of the following exposition can be found in most time series econometrics books.^{10}

From a theoretical point of view, the structural model is the point of departure in the description of a data generating process. Assume a stationary vector x t ( k × 1 ) in which each component in x t is a macroeconomic time series, and that the DGP of these components can be represented by an autoregressive model. To maintain the exposition closest as possible to the actual estimations that follows, assume that vector x t has three components: x t = ( g t , y t , τ t ) ′ , with g t , y t and τ t being time series related with, respectively, government spending, the level of activity (output), and government revenues. The equation below describes x t ’s dynamic by a VAR(p) model, in which p is the order of the model, i.e., the number of past components of x t :

C x t = Φ 0 + Φ ( L ) x t + B ε t Φ ( L ) = ∑ i = 1 p Φ i L i (1)

in which c i j ( i , j = 1 , 2 , 3 ) are the components of the matrix of contemporary correlations C (when i = j , then c i i = 1 )—that is, each component in x t can be affected contemporarily by the other variables contained in vector x t itself; Φ 0 is the vector column whose components are the constant coefficients of each equation and Φ 1 is the (3 × 3) matrix whose components are the past impact coefficients of the macroeconomic variables of vector x t , and ε t = ( ε t g , ε t y , ε t τ ) ′ contains the error terms for each equation. If the autoregressive term in (1) reflects the real DGP, then the components in ε t are not correlated, and can be written as E ( ε t ε ′ t ) = I , in which the standard errors are inserted in the main diagonal of matrix B .

The system of Equation (1) possesses feedbacks: g t , y t and τ t mutually affect each other in terms of past values. But they also can produce contemporary effects through the terms c i j . The error terms in ε t , despite white noise, can have contemporary indirect effects on g t , y t and τ t : ε t τ , for example, can produce contemporary indirect effects on y t and g t through c 23 and c 13 —if these two terms are not equal to zero. The system becomes even more sophisticated more than one type of structural error is allowed to have direct effect on each equation, that is, if the elements outside de main diagonal of B are not equal to zero.

Unfortunately, we cannot estimate the DGP above (the coefficients c i j , ϕ 0 , i and ϕ 1 , i j ) for least squares. The variables g t , y t and τ t produce contemporary impacts among themselves and the OLS estimates of the system suffer from a simultaneity bias: the estimated errors will be correlated between equations. Fortunately, it is possible to transform the system into a manageable form. Multiplying both sides by C − 1 :

x t = A 0 + A ( L ) x t + u t (2)

In which,

A 0 = C − 1 Φ 0

A ( L ) = C − 1 Φ ( L ) e

u t = C − 1 B ε t → C u t = B ε t .

The components of u t are correlated amongst themselves, but they maintain the property of stationarity with an average equal to zero and variances and covariances which are independent of time, that is, E ( u t u ′ t ) = 0 , E ( u t u ′ t ) = Σ u and E ( u t u ′ s ) = 0 ∀ t ≠ s . In general, it is assumed that B is a diagonal matrix which captures the contemporary effects of structural shocks ε t on shocks in a reduced form, u t .

Equation (2) can be estimated by least squares in a consistent form. It was stated in the introduction that autoregressive models in a reduced form cannot be used for economic analysis. The reason is given above: the error terms are not independent shocks of the variables per se; but rather, are a composition of the true structural shocks ε t . Matrices A 0 and A ( L ) contain terms that are compositions of the interaction between contemporary relationships ( C ) and the true structural parameters ( Φ 0 , Φ ( L ) ) . If it is possible to obtain information about the contemporary relationships, imposing a feasible matrix on (2), then it will be able to recover the original model and measure the real impacts of the structural shocks on the system. The estimation by OLS generates parameter estimates (and errors) in accordance with Equation (3) below:

x t = A ^ 0 + A ^ ( L ) x t + u ^ t (3)

In which, E ( u ^ t u ^ ′ t ) = Σ ^ u , and Σ ^ u is symmetric.

Consider now the imposition of a contemporary correlation matrix A on the reduced form model, pre-multiplying both sides of (3) by it. If A = C , the recovered coefficients Φ ^ 0 , Φ ^ ( L ) are estimated in a manner consistent with the structural parameters in (1), the same could be said about the structural errors, ε ^ t . Thus, the problem of identification can be summarized by the choice of matrix A —to the extent that it reflects the real set of contemporary correlations between the endogenous variables of the VAR model.

One possible strategy is to assume that the variables of x t are ordered recursively in terms of contemporary impacts (the Cholesky decomposition). It is assumed that there is a hierarchy between the variables—from the “most exogenous” to the “least exogenous”. In the case where x t = ( g t , y t , τ t ) ′ the most used recursive arrangement in the literature places the variable associated with government spending ( g t ) as the most exogenous (it affects contemporarily the other variables, but is not affected contemporarily by any other variable). Next comes the level of activity ( y t ), contemporarily affected only by the spending variable). Finally comes the variable associated with taxes ( τ t ), which suffers contemporaneous impacts of the two previous variables. This recursive order stipulates a relationship between u ^ t and ε ^ t according to Equation (4):

A u ^ t = B ˜ ε ^ t [ 1 0 0 a 21 1 0 a 31 a 32 1 ] [ u ^ t g u ^ t y u ^ t τ ] = [ b 11 0 0 0 b 22 0 0 0 b 33 ] [ ε ^ t g ε ^ t y ε ^ t τ ] (4)

In the Brazilian literature the ordering in (4) had been used by Cavalcanti and Silva [

Σ ^ u = E ( u ^ t u ^ ′ t ) = ( A − 1 ) B ˜ B ˜ ′ ( A − 1 ) ′ (5)

The symmetrical matrix Σ ^ u —calculated according to (5) and using estimates from (3)—possesses 6 [ = ( k 2 + k ) / 2 ] distinct components, which can be utilized to identify 6 system unknowns in (4), again, k being the number of endogenous variables. The Cholesky ordering, together with the restriction given by B ˜ , guarantees a structural model which can be exactly identified.

In (4) the contemporary impact of output on taxes, a 32 , is determined internally during the identification process. At the same time, the recursive nature of the model restricts the immediate impact of output on government revenues to zero ( a 23 = 0 ). The impact of the level of activity on taxes and spending are also zero ( a 12 = a 13 = 0 ). These last two restriction are actually quite reasonable, when on uses high frequency data: as argued by BP [

BP [

A u ^ t = B ˜ ε ^ t [ 1 0 0 a 21 1 a 23 a 31 a 32 * 1 ] [ u ^ t g u ^ t y u ^ t τ ] = [ b 11 0 0 0 b 22 0 0 0 b 33 ] [ ε ^ t g ε ^ t y ε ^ t τ ] (6)

Thus, a 32 * represents a numerical restriction but, at the same time, not equal to zero as the restriction imposed on government spending.

In Brazil, applications of SVAR models are restricted to national quarterly data that begins with 1995. BP [^{11} Peres then uses a 32 * = 2.03 to identify his structural model. Note that this value implies a high sensitivity of government revenue to economic activity, and very close to BP’s. On the other extreme, Ilzetzki [

In sum, the structural identification approach opens space for various possibilities, depending on key assumption in the identification process. As should be clear by now, at least in small scale fiscal policy autoregressive models, the income-elasticity of taxes is the key parameter for identification. In large scale models, say, when x t = ( g t , y t , τ t , π t , i t ) ′ , π t and i t being the inflation and interest rates, one also has to search for external information about other set of elasticities.^{12} For this study, the analysis focus on the consequences of disturbing parameter a 32 * , and the access the impacts of the sensitivity analysis on tax multipliers. As will be stablished on Section 4, the choice of the output-elasticity of tax revenues will have a direct impact on the identification of the free parameter a 23 , which measures the instantaneous impacts of government revenues on output and, thus, with consequences for the value of the tax multiplier.

The methodological description established the SVAR methodology assuming the use stationary time series. This section describes the data that will be used as proxies for the (theoretical) variables of government spending and revenues, and also output, as well as their statistical characteristics.

Samples of the high frequency macroeconomic series available in Brazil are quite reduced compared to their counterparts in the main developed nations (the main focus of international literature). However, Brazilian samples do make reasonable estimates possible. The Brazilian Institute of Geography and Statistics (IBGE) produces the National Quarterly Accounts (CNT) series, available beginning in 1995. The CNT generates data such as nominal GDP, the real growth rate (“variation in volume”) of GDP proper and GDP categories (consumption, investment, etc.). The volume series (with seasonal adjustment) are available starting in 1996. At most, the CNT database has series with up to 92 observations, from the first quarter of 1995 through the last quarter of 2017. By comparison, US quarterly macroeconomic data dates back at least to the 1950s.

Brazilian fiscal data are less straightforward. There are no official statistics of revenues and expenditures for the Brazilian consolidated government.^{13} In studies analogous to this one, Brazilian researchers face a tradeoff between working with unofficial fiscal estimates—which in general are constructed for specific periods—or work with official data that encompasses the central government,^{14} the latter made available and update on a monthly basis. The National Treasury Secretariat (STN) publishes central government’s “above the line” results (primary results) beginning in January 1997. Consolidation of Treasury’s series makes it possible to form a quarterly sample consisting of 84 observation from 1997 to 2017. The strategy of using central government’s fiscal variables as proxies for consolidated figures has already been used in other empirical works and will also be followed in this study.^{15,16}

Gobetti and Orair [^{17}—distorting the relative proportions of some revenues and expenditures subcategories; second, there is what will be called the amount problem (or, “sum problems”)—which originate from the inclusion, at some point in time, of intra-budgetary operations resulting in the increase of primary revenue and expenditures in the same amount, also not distorting primary result but distorting the level of the series and their dynamic analysis (growth rates); finally, there is the accounting maneuver problem, related to extra-budgetary operations which affect the analysis in terms of the rate of growth of the fiscal series as well as the primary result for various years.^{18} Gobetti and Orair [

In addition to providing an alternative database, Gobetti and Orair’s study [

The capitalization of Petrobrás was an operation that falls into the type described as accounting maneuvers. This operation represented a significant increase in government’s net revenue (R$74.8 billion) and primary spending

(R$42.9 billion). These figures were deduced from the Treasury’s database (as well as other adjustments) for form the new Treasury’s series actually used in the estimations that follows. For the remaining of this article, one should understand mentions to “Treasury” fiscal series as those series already after adjustments; while the “Ipea” series as those produce by Gobetti and Orair [

As mentioned at the beginning of this section, the nominal GDP is available starting in 1995. Real growth rates are available since 1996. From nominal GDP and growth rates with seasonal adjustments one can construct the real GDP at 2017:4 prices. Growth rates without seasonal adjustments and nominal GDP can be combine to derive the quarterly implicit deflator.^{19} The implicit deflator is then used to construct real fiscal series (from both sources) also at 2017:4 prices. Seasonal variations were removed from the fiscal series using ARIMA-X13 method.

In

One more comment should be made about the adjustments made on the fiscal series. The examination of panel (e) reveals the difference in levels between the Treasury and Ipea spending series. This discrepancy is not due only to the incomplete adjustment of the Treasury database, but also because of the different components classifications that form primary spending in both data sources. In fact, panels (e) and (f) do not exhibit the definition of total primary spending: rather, the primary spending series in ^{20}

The next subsection is a brief summary of the statistical properties of all the time series used in the autoregressive models estimated in Section 4. A complete analysis in available upon request.^{21} During the diagnosis, it was verified a sudden change in the DGPs of several series, especially the fiscal series, for the period after 2014—when the recent Brazilian fiscal crisis began. From 2015 onward, with the economy in full recession, GDP and net revenues began to contract continually.^{22} Expenditures did not suffer sudden and continuous contractions, but rather began to exhibit greater volatility than observed up until that point. This unstable dynamics at the end of the sample period is responsible for poorer fit of both univariate and multivariate autoregressive models tried, also affecting formal test of unit root. It’s possible that the recent recession with fiscal crisis has constituted a permanent shock into Brazilian macroeconomic data—a hypothesis that needs to be explored in future research. What the data shows, up until now, is a more sophisticated dynamic in the last period of the complete sample, apparently distinct from the first interval (that is, until 2014). For this study, the option chosen was to perform the analysis for the period before the recent crisis. Thus, the sample period for the unit-root tests of the next subsection and the VAR models of the next section ranges from the first quarter of 1997 to the third quarter of 2014—before the contagion of the fiscal crisis and recession in the last quarter of that year.

The diagnosis of a data generation process defines the way in which variables should be previously transformed, when necessary, before the actual estimation of the VAR model. A mistaken diagnosis of the stochastic characteristics of the components of vector x t (in (3)) would invalidate all of the subsequent analysis. This subsection offers a summary of the unit root tests applied to the fiscal series and output. In panels (a), (c) and (e) of

Unit root tests measure the degree of persistence of a time series. When they are high enough, from a statistical point of view, the degree of persistence indicates a series with a stochastic tendency—i.e., with a unit root. In this case, impacts of shocks suffered by the series will have permanent effects. Contrary, shocks suffered by stationary time series—whether around a tendency or not, whether an ascending or descending trend—dissipate over time. The larger the persistence of a series, the more time it will need to dissipate the shock.^{23}

Let y t be an ordinary time series.^{24} To formally test the degree of persistence in y t , the series can be described as an autoregressive process y t = ρ y t − 1 + z ′ t β + e t , in which z t is a vector whose components are control variables (e.g., constants, tendencies, dummies, etc.). The coefficient ρ measures the degree of persistence which, if close to 1 from the statistical perspective, allows one to affirm the series as a unit root process. Unit root tests test the null hypothesis H 0 : ρ = 1 against the alternative hypothesis H A : ρ < 1 :

H 0 : y t = ρ y t − 1 + z ′ t β + e t H A : y t = ρ y t − 1 + z ′ t β + e t (7)

^{25} In the DF-GLS test, the series passes through a transformation through a regression of generalized least squares before the ADF regression per se. Under the null hypothesis, the parameters estimated by the tests do not possess conventional distributions. The hypothesis tests are realized using specific critical values. The results suggest that GDP and the fiscal variables are highly persistent series. The ϕ statistics of the ADF indicate unit root processes with drift (constant term). In the PP and DF-GLS tests, the null hypothesis is rejected, but only when the alternative includes a tendency.

When structural breaks occur, the power of conventional tests trends towards zero. When they are not explicitly introduced in regressions, the structural breaks produce biases in the coefficient estimates.

The Zivot-Andrews test is an endogenous structural break test because the point of the break is chosen in an optimal manner within the structure of the test itself. This procedure tests the null hypothesis of a unit root against the alternative hypothesis of a structural break, in which the location of the break is tested for all possible periods within a subinterval of the sample (breaks near the extremities are ignored to guarantee a minimum number of observations in each

H_{A}^{5,6} | ADF | PP | DF-GLS | |||||||||
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p^{3} | 𝛄^{4} | 𝝉^{7} | 𝝓^{7} | 𝛒 | 𝛒 | (t-stat) | p | 𝛄^{4} | (t-stat) | 𝛒 | ||

Panel I—IBGE | ||||||||||||

GDP | tend. | 1 | −0.2127 | (−2.93) | (4.38) | 0.79 | 0.87 | (−2.57) | 1 | −0.2036 | (−2.43) | 0.80 |

const. | 1 | −0.006 | (−0.71) | (6.24)** | 0.99 | 1.00 | (0.10) | 1 | −0.0147 | (−0.46) | 0.99 | |

Panel II—National Treasury | ||||||||||||

Net revenues | tend. | 1 | −0.33 | (−2.34) | (3.52) | 0.67 | 0.49 | (−4.56)*** | 1 | −0.22 | (−1.97) | 0.78 |

const. | 1 | −0.05 | (−1.65) | (3.78) | 0.95 | 0.95 | (−1.95) | 1 | 0.01 | (−0.59) | 1.01 | |

Primary expenses | tend. | 1 | −0.22 | (−2.25) | (2.75) | 0.78 | 0.73 | (−3.33)* | 0 | −0.27 | (−3.25)** | 0.73 |

const. | 1 | −0.01 | (−0.93) | (12.5)*** | 0.99 | 0.99 | (−0.42) | 0 | 0.02 | (1.82) | 1.02 | |

Discretionary expenses | tend. | 1 | −0.22 | (−2.30) | (2.83) | 0.78 | 0.80 | (−2.66) | 0 | −0.19 | (−2.57) | 0.81 |

const. | 1 | −0.01 | (−0.30) | (1.80) | 0.99 | 0.98 | (−0.34) | 0 | 0.00 | (0.05) | 1.00 | |

Mandatory expenses | tend. | 1 | −0.05 | (−0.86) | (2.31) | 0.95 | 0.88 | (−1.76) | 4 | −0.05 | (−0.78) | 0.95 |

const. | 1 | −0.02 | (−2.11) | (21.2)*** | 0.98 | 0.99 | (−1.17) | 3 | 0.01 | (1.35) | 1.01 | |

Panel III—Ipea | ||||||||||||

Net revenues | tend. | 1 | −0.31 | (−2.14) | (3.06) | 0.69 | 0.50 | (−4.48)*** | 1 | −0.18 | (−1.73) | 0.82 |

const. | 1 | −0.04 | (−1.58) | (4.00)* | 0.96 | 0.95 | (−2.09) | 1 | 0.01 | (0.71) | 1.01 | |

Primary expenses | tend. | 1 | −0.21 | (−2.20) | (2.53) | 0.79 | 0.76 | (−3.13) | 3 | −0.30 | (−3.37)** | 0.70 |

const. | 1 | −0.01 | (−0.74) | (10.9)*** | 0.99 | 0.99 | (−0.69) | 3 | 0.02 | (1.62) | 1.02 | |

Costs and Investments | tend. | 8 | −0.20 | (−1.77) | (2.27) | 0.80 | 0.78 | (−2.66) | 0 | −0.20 | (−2.21) | 0.80 |

const. | 8 | 0.02 | (−0.32) | (1.63) | 0.98 | 0.97 | (−0.47) | 1 | 0.03 | (0.77) | 1.03 | |

Other expenses | tend. | 1 | −0.05 | (−0.77) | (2.25) | 0.95 | 0.88 | (−1.80) | 4 | −0.04 | (−0.70) | 0.96 |

const. | 1 | −0.02 | (−2.08) | (22.5)*** | 0.98 | 0.99 | (−1.75) | 3 | 0.01 | (1.31) | 1.01 |

Source: Prepared by the authors. Notes: 1) *p < 0.1; **p < 0.05; ***p < 0.01. 2) Tests applied in logarithmic transformations of levelled series. 3) p is the number of lags of the terms Dy used in the regressions. 4) In the ADF and DF-GLS tests, the regressions have the format Δ y t = γ y t − 1 + x ′ t β + e t , in which γ = ρ − 1 . The null hypothesis H 0 : γ = 0 is equivalent to H 0 : ρ = 1 . 5) H A : y t = a 0 + ρ y t − 1 + x ′ t β + e t , in which x t contains past terms Δ y t − i (ADF and DF-GLS). 6) H A : y t = a 0 + ρ y t − 1 + x ′ t β + e t , in which x t contains past terms Δ y t − i (ADF and DF-GLS). 7) If H A has a tendency, the columns τ and ϕ express the statistics τ τ ( H 0 : γ = 0 )and ϕ 3 ( H 0 : γ = a 2 = 0 ); if H A contains just one constant, the columns τ and ϕ exhibit the statistics τ μ ( H 0 : γ = 0 ) and ϕ 3 ( H 0 : γ = a 0 = 0 ).

H_{A} | k = 0 | k = 2 | k = 4 | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Break | 𝛒 | (t-stat) | Break | 𝛒 | (t-stat) | Break | 𝛒 | (t-stat) | ||

Panel I—IBGE | ||||||||||

GDP | both | 1997:4 | 0.80 | (−3.27) | 1997:4 | 0.79 | (−3.36) | 1998:2 | 0.78 | (−3.12) |

tend | 1998:4 | 0.80 | (−3.09) | 2001:3 | 0.70 | (−3.09) | 1998:4 | 0.79 | (−2.90) | |

const | 1997:4 | 0.80 | (−3.29) | 2006:4 | 0.77 | (−3.68) | 2006:4 | 0.77 | (−3.40) | |

Panel II—National Treasury | ||||||||||

Net revenues | both | 2008:3 | 0.08 | (−7.42)*** | 2008:3 | −0.03 | (−4.85)* | 2008:3 | −0.05 | (−3.53) |

tend | 2008:1 | 0.11 | (−7.18)*** | 2008:1 | 0.02 | (−4.62)** | 2008:1 | −0.01 | (−3.45) | |
---|---|---|---|---|---|---|---|---|---|---|

const | 2012:1 | 0.25 | (−6.34)*** | 2012:1 | 0.32 | (−3.70) | 2012:2 | 0.45 | (−2.39) | |

Primary expenses | both | 2005:3 | 0.60 | (−4.21) | 2005:3 | 0.55 | (−3.98) | 2005:3 | 0.47 | (−4.17) |

tend | 1999:1 | 0.69 | (−3.68) | 1998:4 | 0.67 | (−3.45) | 2010:1 | 0.55 | (−4.01) | |

const | 2005:3 | 0.60 | (−4.24) | 2005:3 | 0.55 | (−4.07) | 2005:3 | 0.44 | (−4.49) | |

Panel III—Ipea | ||||||||||

Net revenues | both | 2008:3 | 0.13 | (−7.13)*** | 2008:3 | 0.05 | (−4.60) | 2007:1 | 0.11 | (−3.24) |

tend | 2008:1 | 0.14 | (−7.00)*** | 2011:2 | 0.19 | (−4.50)** | 2008:1 | 0.13 | (−3.14) | |

const | 2012:1 | 0.26 | (−6.35)*** | 2012;1 | 0.32 | (−3.79) | 2012:1 | 0.48 | (−2.42) | |

Primary expenses | both | 2005:3 | 0.62 | (−4.15) | 2005:3 | 0.62 | (−3.42) | 2008:2 | 0.52 | (−4.06) |

tend | 1999:1 | 0.72 | (−3.54) | 1998:4 | 0.73 | (−2.97) | 2010:1 | 0.61 | (−3.74) | |

const | 2005:3 | 0.63 | (−4.20) | 2005:3 | 0.62 | (−3.60) | 2005:3 | 0.52 | (−4.14) |

Source: Prepared by the Authors. Notes: 1) *p < 0.1; **p < 0.05; ***p < 0.01. 2) Tests applied in logarithmic transformations of levelled series.

of the partitions). The point chosen for the break is that which generates a coefficient ρ most unfavorable for the null hypothesis, i.e., which generates a t-statistic as low as possible. On the other hand, the ρ coefficient possesses its own distribution with higher critical points and broader intervals of confidence, which make it difficult to reject the null hypothesis in comparison with traditional tests. Also, the Zivot-Andrews test regressions can contain control regressors of past terms of the first difference between y t , and Δ y t − i . It is convenient to choose the optimal number of past terms k, through information criteria. The inclusion of the past terms seeks to establish a regression with a better fit and stationary residuals.

In the ^{26} (SBC) chooses k = 0 for all of the tested series. The null hypothesis of the unit root is not rejected by the GDP and the two series of primary spending. Net revenues from both sources (Ipea and the Treasury), would be compatible with stationary processes around the tendencies with structural breaks. This result, if true, would demand different transformations between the series included in the estimated VAR models. A detailed analysis of these tests could alter this preliminary conclusion.

The standard procedure of transforming series with stochastic tendencies into stationary series is based on the application of the operator on the first difference. Returning to understand x t = ( g t , y t , τ t ) ′ as a vector of endogenous variables from a VAR model of fiscal policy, as already put forth in the methodology, with the components g t , y t and τ t representing the series associated with the government’s primary expenses, GDP and net revenues, these variables should not be inserted on a level, but rather as variation rates (i.e., the first difference of the logarithms).^{27} The use of growth rates offers the additional benefit that the matrix components of contemporary correlations A can now be interpreted as elasticities.

In addition to the results of this sensitivity analysis of the tax income-elasticity parameter in terms of the components of the matrix of contemporary correlations, this section also exhibits impulse-response functions for fiscal shocks, with an emphasis on output responses—to tax shocks under the various hypotheses. Based on IRFs, fiscal multipliers were also calculated and are displayed in

During Section 2, we argued that the income-elasticity parameter for revenues was estimated in previous works to be between 0.76 [^{28}

a_{ij} | |a_{32}| (income-elasticity of revenues) | ||||||
---|---|---|---|---|---|---|---|

=0.25 | =0.75 | =1.25 | =1.75 | =2 | =2.5 | =3 | |

(A) National Treasury | |||||||

a_{21} | −0.08 | −0.1* | −0.11* | −0.13** | −0.14** | −0.16** | −0.19** |

(0.05) | (0.06) | (0.06) | (0.06) | (0.06) | (0.07) | (0.08) | |

a_{31} | −0.47** | −0.42** | −0.36* | −0.31 | −0.28 | −0.23 | −0.18 |

(0.21) | (0.21) | (0.21) | (0.21) | (0.21) | (0.22) | (0.23) | |

a_{32} | −0.25 | −0.75 | −1.25 | −1.75 | −2 | −2.5 | −3 |

a_{23} | −0.06** | −0.02 | 0.01 | 0.05 | 0.07* | 0.11** | 0.16** |

(0.03) | (0.03) | (0.03) | (0.04) | (0.04) | (0.05) | (0.06) | |

(B) Ipea | |||||||

a_{21} | −0.11* | −0.13** | −0.14** | −0.16** | −0.16** | −0.18** | −0.2** |

(0.06) | (0.06) | (0.06) | (0.07) | (0.07) | (0.07) | (0.08) | |

a_{31} | −0.32 | −0.26 | −0.19 | −0.13 | −0.1 | −0.03 | 0.03 |

(0.21) | (0.21) | (0.21) | (0.21) | (0.22) | (0.23) | (0.24) | |

a_{32} | −0.25 | −0.75 | −1.25 | −1.75 | −2 | −2.5 | −3 |

a_{23} | −0.05* | −0.01 | 0.03 | 0.07* | 0.1** | 0.14** | 0.2** |

(0.03) | (0.03) | (0.04) | (0.04) | (0.04) | (0.05) | (0.06) |

Source: Prepared by the authors. Notes: 1) Standard errors (se) in parentheses. 2) * a i j e p [ a i j ] > 1.46 ; ** a i j e p [ a i j ] > 1.96 ; a i j e p [ a i j ] > 2.33 .

compatible with various interpretations of the effectiveness of fiscal policy. The larger the (assumed) value of contemporary impact of the economic cycle on government revenues, the larger the contemporary impact of the tax shock will be on its own level of activity. This relationship is identified in both estimates with the two sources of available fiscal data. In

Very low values for the income-elasticity of government revenues (i.e., a 32 between −0.75 and −0.25) generate counter-intuitive estimates in relation to the instantaneous impact of taxes themselves on GDP: the values of a 23 in these cases are indicative of an instantaneous positive response of output to tax shocks. Intermediate values of a 32 are associated with the a 23 coefficients with the expected sign but, in general, without statistical significance. Only when the elasticity of a 32 is high—equal or above 2—is the tax impact significant. The values of these various estimates of matrix A will have an impact on their respective impulse-response functions for fiscal shocks.

(b), (c) and (d)] and government spending shocks [panels (e) and (f)]. The IRFs displayed are the Wold’s representations of structural models, which were derived from the first-order reduced-form VAR models, whose estimates produce stationary errors without serial correlations and parameters which guarantee stability. The estimation of the VAR(1) model produces coefficient and regression error estimates, x t = A ^ 0 + A ^ 1 x t − 1 + u ^ t . Imposing on the estimates the matrices A and B ¯ it is possible to recover the structural coefficients, x t = Φ ^ 0 + Φ ^ 1 x t − 1 + ε ^ t , with Φ ^ 0 = A A ^ 0 , Φ ^ 1 = A A ^ 1 and ε ^ t = ( B ¯ ) − 1 A u ^ t . The solution of the model is given by:

x t = u ^ + ∑ i = 0 ∞ ψ i ε ^ t − i u ^ = A ^ 0 / ( I − A ^ 1 ) ψ ^ i = ( A − 1 ) B ¯ A 1 i (8)

in which ψ ^ i = ∂ x t + i / ∂ ε ^ t ; the terms ψ ^ i ( i = 1 , 2 , ⋯ ) form the IRF.

^{29} By definition, the relationship

t | 𝝉 | g^{(1)} | ||||||
---|---|---|---|---|---|---|---|---|

|a_{32}| = 0.25 | |a_{32}| = 0.75 | |a_{32}| = 1.25 | |a_{32}| = 1.75 | |a_{32}| = 2 | |a_{32}| = 2.5 | |a_{32}| = 3 | ||

(A) National Treasury | ||||||||

0 | 0.32 | 0.32 | −0.06 | −0.28 | −0.39 | −0.64 | −0.90 | 0.71 |

1 | 0.85 | 0.85 | 0.03 | −0.62 | −1.05 | −2.30 | −4.55 | 1.69 |

2 | 0.55 | 0.55 | 0.00 | −0.36 | −0.56 | −1.04 | −1.63 | 1.63 |

3 | 0.69 | 0.69 | 0.01 | −0.46 | −0.76 | −1.49 | −2.54 | 1.64 |

4 | 0.61 | 0.61 | 0.01 | −0.40 | −0.64 | −1.21 | −1.97 | 1.66 |

5 | 0.65 | 0.65 | 0.01 | −0.43 | −0.70 | −1.35 | −2.23 | 1.64 |

6 | 0.63 | 0.63 | 0.01 | −0.41 | −0.66 | −1.27 | −2.09 | 1.65 |

7 | 0.64 | 0.64 | 0.01 | −0.42 | −0.68 | −1.31 | −2.16 | 1.65 |

8 | 0.64 | 0.64 | 0.01 | −0.42 | −0.67 | −1.29 | −2.12 | 1.65 |

9 | 0.64 | 0.64 | 0.01 | −0.42 | −0.68 | −1.30 | −2.14 | 1.65 |

10 | 0.64 | 0.64 | 0.01 | −0.42 | −0.67 | −1.30 | −2.13 | 1.65 |

(B) Ipea | ||||||||

0 | 0.29 | 0.07 | −0.16 | −0.41 | −0.54 | −0.82 | −1.13 | 0.87 |

1 | 0.79 | 0.33 | −0.32 | −1.31 | −2.02 | −4.34 | −10.0 | 1.40 |

2 | 0.49 | 0.17 | −0.21 | −0.66 | −0.92 | −1.54 | −2.33 | 1.41 |

3 | 0.64 | 0.25 | −0.26 | −0.93 | −1.36 | −2.51 | −4.33 | 1.42 |

4 | 0.54 | 0.20 | −0.23 | −0.76 | −1.07 | −1.86 | −2.93 | 1.43 |

5 | 0.60 | 0.22 | −0.24 | −0.85 | −1.22 | −2.19 | −3.60 | 1.42 |

6 | 0.57 | 0.21 | −0.23 | −0.79 | −1.13 | −1.98 | −3.18 | 1.43 |

7 | 0.58 | 0.22 | −0.24 | −0.82 | −1.18 | −2.09 | −3.41 | 1.42 |

8 | 0.57 | 0.21 | −0.23 | −0.81 | −1.15 | −2.03 | −3.27 | 1.42 |

9 | 0.58 | 0.22 | −0.24 | −0.82 | −1.17 | −2.07 | −3.35 | 1.42 |

10 | 0.57 | 0.21 | −0.24 | −0.81 | −1.16 | −2.05 | −3.31 | 1.42 |

Source: Prepared by the authors. Note: The spending multiplier is in accordance with the structural model | a 32 | = 2 .

found between parameter a 32 and a 23 is extended to tax multipliers: for both the impact of the fiscal shock as well as the cumulative shock, the multiplier will be greater (in magnitude) the larger the sensitivity to government revenues in the economic cycle. When a 32 > 2 , the tax multiplier tends to approximate the spending multiplier and may surpass it (in magnitude) depending on the fiscal data sample used.

The question of which fiscal instrument is the most effective (i.e., its ability to affect output in the short term) is present, in one form or another, in almost all empirical works that measure multipliers. The conclusion of Blanchard and Perotti [^{30} In the structural VAR model the central question should be: what should be the value chosen for the parameters of income-elasticity of tax revenues? To the authors of this study the evidence so far points to a large value, probably between 2 and 2.5. This being the case, one can argue that Brazilian tax multiplier is of the same order of magnitude as the spending multiplier; that is, there isn’t a single fiscal instrument unequivocally more efficient than the other. If | a 32 | is in fact between 2 and 2.5, the instantaneous tax multiplier is estimated between −$0.4 and −$0.8; the cumulative multiplier attaining values between −$0.7 and −$2 in 10 months. When | a 32 | = 2 , the Treasury sample implies tax multiplier lower than the spending multiplier; the Ipea sample would suggest the opposite.

^{31}

All in all, the results found and summarized in

This study presents measures of the effects of fiscal shocks on Brazil’s GDP—with focusing on tax shocks and assuming different hypotheses of identification in the SVAR model. The hypotheses are related to the value of the instantaneous elasticity of government revenues in relation to output. The estimations used quarterly data from 1997:1 to 2014:3 and two sets of fiscal variables: the official data from National Treasury (with adjustments) and an alternative database detailed in Gobetti and Orair [

The value of the instantaneous sensitivity of government revenues in relation to output is the key parameter used to determine the tax multiplier. There is a correlation between this parameter and the instantaneous effect of taxes on the level of activity itself, attested by the estimates of the contemporary correlation matrices (i.e., the structural matrices) of the SVAR models. When the income-elasticity of taxes is high, there is a tendency to the tax-elasticity of output also to be high. This latter elasticity defines, to a great extent, the initial dynamic of the output response to tax shocks.

In qualitative terms, these results are in line with most of the applied studies in Brazil. The fiscal shocks generate traditional Keynesian effects: the level of activity grows by virtue of a government spending shock and decreases by virtue of shocks in government revenues. However, the focus of this study is the relationship between the magnitude of the response of economic activity (to the tax shock) and the hypotheses regarding the parameter which measure the income-elasticity of government revenues. The values assumed for this elasticity parameter vary from a floor of 0.25% to a maximum of 3%. This interval encompasses the values used in other studies in Brazilian literature. When the SVAR model is identified with a low value for this referenced elasticity, the tax shocks generate output responses that are not significant; when the elasticity is large (above 2%), tax shocks cause negative and significant output responses that are stronger (in absolute value) than those found by other studies.

As a rule, (tax and spending) impact multipliers are below one. The exception occurs when the income-elasticity of tax revenues is equal to 3% in one of the fiscal series. In the extreme case the cumulative tax multiplier ten months after the shock reaches a value above −$3. When more modest hypotheses are adopted (i.e., an output-elasticity of revenues between 2 and 2.5), the tax (impact) multipliers remains within the range of −$0.4 and −$0.8. The spending multiplier, in turn, remains between $0.7 and $0.9. After 10 periods, the cumulative had substantial increase. Even though these should be interpreted with care—impulse-response functions are largely statistically insignificant after the first period beyond the initial shock—, one should note that, still with modest hypothesis of output-elasticity of taxes, tax multipliers and spending multipliers can reach −$2 and −$1.6, respectively.

The authors declare no conflicts of interest regarding the publication of this paper.

Barros, G.S., and Correia, F.M. (2019) Fiscal Multipliers in Brazil: A Sensitivity Analysis on the Structural Identification Procedure. Modern Economy, 10, 2175-2200. https://doi.org/10.4236/me.2019.1010137