Fiscal Multipliers in Brazil: A Sensitivity Analysis on the Structural Identification Procedure

ABSTRACT

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.

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 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 [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 ${x}_{t}\left(k\times 1\right)$ 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: