ME  Vol.10 No.10 , October 2019
Fiscal Multipliers in Brazil: A Sensitivity Analysis on the Structural Identification Procedure
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.

1. Introduction

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 [2] ; the level of public debt [3] ; the conduction of monetary policy;1 the phase of the economic cycle [4] and the past trajectory of public spending itself [6].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. [9] (sign-restriction approach), Cavalcanti and Silva [8], Pires [10] and Oreng [11] (SVAR).5 Peres and Ellery Jr. [12] rely on the structural identification procedure of Blanchard and Perotti [5] (henceforth, BP [13] ) and find traditional Keynesian effects with statistical significance. More recent works do estimate the value of the multiplier. Focusing on tax multipliers, Pires [14] uses a Markov-switching model and finds an impact tax multiplier between −$0.2 and −$0.3. Matheson and Pereira [15] estimate the accumulated tax multiplier in a Cholesky decomposition, with estimating ranging from −$0.5 (one year) and −$2 (two years). Castelo-Branco et al. [16] uses a MS-SBVAR, obtaining impact multipliers around −$0.12 and −$0.14. These values are the monetary response of GDP for each $1 increase in tax revenues. As mentioned, these values are usually inferior to the spending multipliers. Putting the numbers in perspective, the public spending multiplier calculated by Castelo-Branco et al. can reach $1.7 (for government’s investment spending).

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 [13], assuming various hypothesis for the aforementioned key-parameter. As will be seen in the following, the value one assumes for the income elasticity of tax revenues largely determines the impulse-response function of the tax shocks and, therefore, the tax multipliers.

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 [13] inaugurated an additional strategy, imposing a specific value for one of the correlations of their three-endogenous variables model (government spending and revenues and output). This key contemporaneous correlation parameter was the income-elasticity of tax revenue.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. [12] and Mendonça et al. [17]. The former estimated the income-elasticity of tax revenues for the period 1994-2005, finding values very close to the BP’s own estimates for the United States; the latter imposed a limited number of values, drawn from empirical SVAR studies from other countries,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 output8 (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 [1]. This latter database was the result of adjustments on the official data, correcting several issues, from government’s revenues and spending classification errors to more serious extra-budgetary problems which alter government’s primary results—such the so-called fiscal manipulations (i.e., “pedaladas fiscais”). The authors of this study also produced some adjustments in the official Treasury data (making them more in line with Ipea’s series), correcting for the most obvious problems. The methodology of Gobetti and Orair [1], however, is the most complete set of adjustments known to date.

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 [1]. Section 4 presents the findings, the impulse-response functions from the fiscal shocks and the fiscal multipliers from spending and (several types of) tax shocks. The last section concludes.

2. Methodology

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 , ns 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 Table 3, the asterisks indicate cases in which the ratio between the estimated coefficients a i j ( i , j = 1 , 2 , 3 ) and their respective standard errors generate estimates which exceed the critical values of the t-student table (for large samples).

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.

Figure 2 displays the impulse-response functions for tax shocks [panels (a),

Figure 2. IRFs of fiscal shocks. Source: Prepared by the authors. Notes: 1) Confidence intervals (CI) for a bootstrap of 200 repetitions. 2) Traced lines: CI of 95%. 3) Line with points: CI of 90%.

(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.

Figure 2 displays the output responses (y) to fiscal shocks (in τ or g). The panels on the left represent the IRFs using fiscal data from the Treasury; the panels on the right use the fiscal data from Ipea. The panels (a) and (b) [(e) and (f)] exhibit the response of output to the tax [spending] shock, in accordance with the structural models assuming a 32 = 0.75 (black) and a 32 = 2 (gray). Panels (c) and (d) show that there is the aforementioned correlation between the magnitude of output’s response to a tax shock and the value of a 32 : the larger the magnitude of the restricted parameter, the more negative the output’s response will be. In the Treasury estimates, the output response is not significant at 10 percent, even when a 32 = 2 ; with the Ipea data, the response is marginally significant at 5 percent for the same restriction. When a 32 > 2 , the tax shock generates significant GDP responses in both samples. The lower panels of Figure 2 display the responses of output to a shock in government expenses, which are significant at 5 percent (marginally). The sensitivity analysis for a 32 does not have large effects on output’s response to spending shocks. Also, when using the first order model, the impulse-response functions of all the fiscal shocks have little persistence over the long-term and dissipate rapidly.

Table 4 displays the fiscal multipliers calculated based on the IRFs. The values are the result of the interaction between the ψ ^ i coefficients and the average values of GDP, and the government’s revenues and expenses. In Table 4 the tax multipliers are calculated for the structured models already reported in Table 3 and panels (c) and (d) of Figure 2. In the last column of Table 4 we relate the government spending multipliers just for the structural model | a 32 | = 2 . The impact multipliers are on line t = 0 . The other lines exhibit the cumulative multipliers up to t quarters after the initial shock.29 By definition, the relationship

Table 4. Fiscal multipliers.

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 [13] is that [for the United States] spending is more effective than taxes in shifting aggregate demand and output. The opposite conclusion was drawn by Mountford and Uhlig [29] —using the same database as BP [13] by different identification methodology. This study shows that even within SVAR methodology, for the Brazilian economy at least, the answer to this controversy depends on basic assumptions about tax revenues summarizes in the structural matrix of the model.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.

Table 4 summarizes the results of this article. Spending multipliers tends slightly lower than unit at impact. These results are in line with government’s consumption multipliers estimated by Pires [14] and Castelo-Branco et al. [16] ; and well above those calculated by Peres e Ellery [12], Mendonça et al. [17] and Oreng [11]. The long run multipliers (10 quarters) tend to be well above unit. The impact multipliers carry more confidence since the impulse-response functions tend to be statistically significant at the impact and at most on next period. The same is true for tax multipliers. More importantly, the tax multipliers—the focus of this study—are shown to be substantial when income-elasticity of government revenues are high. Assuming | a 32 | = 2.5 , the impact tax multiplier is well above calculation from other studies in the Brazilian literature reviewed by the authors. In fact, the results found here puts tax policy at least as equally effective as spending policy.31

All in all, the results found and summarized in Table 4 attest to the importance of a precise estimation of the key-parameter of the structural VAR fiscal policy models in Brazil: the income-elasticity of tax revenues. Later studies can, and should, refine the discussion above with updated estimated of the key-parameters. In addition, one can argue that the focus on the income-elasticity of tax revenues raised another dispute: about the level and composition of the tax burden. Surely the characteristics of the tax burden will have impacts on the aforementioned parameter through the effects on the marginal tax burden. In recent decades, for example, there has been a strong rise in Brazilian total tax burden: going from values close to 23% of GDP (at the end of the 1980s) to roughly 35% at the beginning of the current decade [31]. At the same time, there is evidence that the tax burden general trend has been relatively more pronounced on those in the lower income brackets [32]. Combined, these trends (level and distribution of the tax burden) can have important impacts on the marginal tax burden—which must have influence on the magnitude of the tax multiplier. It can be argued that the marginal tax burden will suffer even further alterations when (and if)—to the extent that the country displays sustained economic growth—significant portions of the population change their income levels and possibly their average tax burden (considering no tax reform). Those questions do not have a categorical response at this point, and should encourage new discussion of the Brazilian tax system and its effects on the effectiveness of fiscal policy. In sum, the debate about the tax burden is not just whether it is high or low, according to some criterion (e.g., distortions, incentives, income distribution, etc.), but also whether the arrangement has some impact on the ability of the government to promote effective measures to stabilize output.

5. Conclusions

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 [1], correcting problems and distortions within the official database (including the extra-budgetary operations that distorted primary surplus for some years).

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.


1There is some evidence that accommodating monetary policy in developed countries (in macroeconomic environments resembling liquidity trap and of lower-bound interest rates), particularly after the international financial crisis, can increase the effectiveness of fiscal policy. See Blanchard and Leigh [5].

2Cavalcanti [7] offers a brief review of the literature pointing out the main methodological approaches used to calculate fiscal multipliers (using macroeconomic time series), as well as the main (characteristic) determinants for multiplier values.

3That is, positive spending shocks generate positive responses of output levels; and positive tax shocks generate negative responses of output.

4See Cavalcanti and Silva [8] and Mendonça et al. [9].

5In most cases by simple Cholesky ordering.

6The output-elasticity of government’s revenues or, yet, the elasticity of government revenues to output.

7Beside the values from BP [13] for the United States, Mendonça et al. [17] uses parameter values from empirical studies from Spain, Slovenia and the European Union, and also compares the SVAR approach with other identification strategies (signal restrictions and threshold-VAR).

8The government revenues-elasticity of output or, yet, the elasticity of output to government revenues.

9An income-elasticity of government revenues of 2% (or, simply, 2) means that for a 1% increase in real output real revenues rise by 2%.

10See, for example, Enders (2015, Ch. 5) [18], Lütkepohl and Krätzig (2004, Ch. 3-4) [19] and Lütkepohl (2006, Ch. 2-4, 9) [20].

11One should note that income-elasticity of government revenues being equal to 2.03 simples affirming that the contemporary effect of elevating output on revenues is positive. In the matrix form of (6), this means that the term a32 is negative. Greater attention should be given to the interpretation of the estimated parameters in the results section.

12See Perotti [23] for an analysis of the SVAR model with the five mentioned variables, and the strategies for restricting the key parameters. Medonça et al. [17], in addition to the small model with three variables, also estimate a model with five variables with an analogous identification procedure.

13Consolidated government: encompasses the three spheres of government in Brazil: federal, state and municipal (local) governments.

14Central government: federal government (National Treasury), Social Security and the Central Bank.

15See Peres [21], Peres and Ellery Jr. [12], Ilzetzki [22] and Matheson and Pereira [15] for examples of applications using central government’s figures.

16Another less attractive possibility is to use Brazilian National Account’s public sector series—“net government income” and “government consumption”—available from IBGE’s quarterly national accounts. However, this alternative results in further miss specification since a substantial part of government spending is computed as transfers to the private sector and included as private income and consumption (and not on government accounts). This is the case of social benefits (pensions, retirement benefits, low-income social benefits, etc.), which sums’ to almost half of the central government’s expenditures. Concomitantly, public investment is computed together with private investment in one spending category called “gross formation of fixed capital” (FBCF). These IBGE series had been used in other empirical works, together with unofficial estimates of government’s revenues and expenditures. Santos et al. [24] estimated the net tax burden of the Brazilian consolidated government for the period between 1996 and 2009; Santos et al. [25] estimated public sector’s spending in gross fixed capital formation that can be combined with IBGE’s consumption series. Mendonça et al. [9], Pires [14] and Grudtner and Aragon [26] are examples of applications mixing official and unofficial fiscal series.

17Net revenue is defined as total revenues minus transfers to states and municipalities (constitutional or voluntary). This is the quantity of financial resources that the federal government has available to pay for its expenses. In this paper the term “net revenue” will be used together with “primary revenue” interchangeably.

18Including into these extra-budgetary procedures there are those that became known in the Brazilian press as fiscal pedaling (“pedaladas fiscais”). One example of this kind of procedure is what happened during some years, and masked central government’s primary result, that is, the delaying of transfers of resources t public banks, referring to disbursement made by the banks in the name of the government to pay for subsidies of social programs. When the federal government finally honored these commitments with these financial institutions in 2015, these expensed entered into the accounting of the Treasury’s cash flow.

19That is, the implicit deflator (inflation measure) in relation to the previous quarter. The implicit deflator published by IBGE does not measure quarterly inflation, but rather the variation in prices during the quarter in relation to the average prices of the previous year.

20Given the amount of adjustments necessary on the fiscal series, a complementary material to accompany this article is available upon request. The extra material describes in more detail the two fiscal databases, adjustments and expenditures subcategories for each source.

21Reference to the complementary material. See previous footnote.

22Net revenues begin to fall before the beginning of the economic recession, and later became stagnant at a very low level.

23See Enders (2015, p. 181-89) [18] for a succinct description of the characteristics of a series with a stochastic and determinist tendency.

24Not necessarily the output, as in the methodological section.

25Also known as ERS test.

26Schwartz Bayesian Criterion (SBC).

27For a better exposition of the results, the rates have been multiplied by 100.

28Since the dummy variables represent exogenous events—whether they have to do with fiscal policy or output—in the VAR model with dummies it was not necessary to have an identification strategy for the matrix of contemporary correlations: the dummy coefficient already represents exogenous effects; and the impulse-response functions derived from them correspond to the system’s structural responses.

29The accumulated multiplier for period t is given by the ratio of the present value of the monetary flow implicit in the IRFs of output (y) until period t and the present value of IRFs of the fiscal impulse (either t or g). The discount for real interest rates during the period from 1997 to 2014 is given by the difference between the basic Selic rate and the inflation rate from Brazilian official consumer price index (IPCA). The Selic and IPCA monthly data can be obtained online through Ipeadata website.

30Caldara and Kamps [30] try to reconciliate the apparently divergent results between the SVAR methodology and the sign restriction approach (US data). Both methodologies can arrive at similar results, depending on the restrictions made on the structural matrix of the SVAR model. In other words, there is a SVAR identification which can be compatible with the results of other approaches. The work of Caldara and Kamps is, in part, a test of sensitivity which is analogous to the present study.

31The complementary material referred earlier also brings summary tables of the relevant empirical literature of fiscal policy in Brazil.

Cite this paper
da Silveira Barros, G. and Correia, F. (2019) Fiscal Multipliers in Brazil: A Sensitivity Analysis on the Structural Identification Procedure. Modern Economy, 10, 2175-2200. doi: 10.4236/me.2019.1010137.
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