How Financial Stress Can Impact Fiscal and Monetary Policies: Threshold VAR Analysis for Brazilian Economy

Abstract

This study examines economic policy responses in Brazil during periods of financial stress, with a particular emphasis on the dynamics of both the impulse and rule components of fiscal policy. We offer novel empirical evidence on policy responses under both low and high stress conditions, utilizing monthly data that span the past two decades. To this end, we construct a Financial Stress Index (FSI) and integrate it into a threshold-VAR framework. Additionally, we employ five distinct methodologies to decompose fiscal policy into its impulse and rule components. Our analysis yields two main findings. First, fiscal policy exhibits procyclical behavior in its impulse component and countercyclical behavior in its rule component across both regimes. Second, while monetary policy is countercyclical during high stress conditions, its impact remains largely statistically non-significant. These results suggest that policymakers should exercise caution when timing the implementation of expansionary fiscal policies, carefully considering the phase of the business cycle. Moreover, our findings carry significant implications for the ongoing discourse on fiscal stimulus and debt stabilization strategies, particularly in the context of financial stress.

1. Introduction

The debate on the role of fiscal policy as a stabilizing instrument for output fluctuations remains ongoing. This debate was significantly amplified by the global economic crisis that began in 2008 and the subsequent COVID-19 pandemic (Davoodi et al. 2022). These events underscored the limitations of orthodox monetary policy tools as many central economies had nearly exhausted these measures with interest rates already close to zero, which further highlights the critical role of fiscal policy.

The fiscal authority is expected to exhibit countercyclical policies, particularly during recessions (Claessens et al. 2009). Ideally, the government should increase spending during economic downturns and reduce it during upturns, thereby stabilizing output fluctuations (OCDE 2003). However, policymakers may sometimes respond procyclically during periods of economic growth, creating asymmetry and exacerbating the business cycle. This means deficits increase during recessions but do not decrease during growth periods, resulting in an asymmetric impact on the business cycle.

Recent literature highlights the significant role of fiscal and monetary policy uncertainty in causing economic and financial disruptions. The authors in Hong et al. (2024) introduce a novel news-based measure of Fiscal Policy Uncertainty across 189 countries, showing its substantial contractionary effects such as decreased industrial production in both Advanced and Emerging Economies. The authors in Aizenman et al. (2024) discuss the challenges for Emerging Economies amid high global financial uncertainty, inflation, and rising debt-to-GDP ratios post Global Financial Crisis and $\mathrm{COVID}$-19 pandemic. They emphasize the exacerbated vulnerabilities due to global monetary tightening and suggest strengthening domestic macroeconomic fundamentals. Other authors have examined how fiscal and monetary policies in Emerging Economies respond to increased economic and financial uncertainty during recent crises, such as the $\mathrm{COVID}$-19 pandemic and the Russia–Ukraine conflict (see, for example, Lastauskas and Nguyen 2024; Makololo and Seetharam 2020, among others).

This paper investigates fiscal policy asymmetries in Brazil, a nation with one of the largest debt-to-GDP ratios among Emerging G20 Countries (IMF 2024). First, we use techniques to decompose fiscal variables into rule and impulse components to ascertain whether these components exhibit symmetry during periods of high and low financial stress. Additionally, we analyze the response of monetary policy during these times.

Shortly before the 2008 financial crisis, Brazil achieved investment-grade status as a result of sustained fiscal and monetary policy efforts. These efforts included measures adopted from 1999 onwards, such as inflation targeting, a floating exchange rate, and the introduction of the Fiscal Responsibility Law (Holland 2019). However, there is consensus that Brazil faces a chronic fiscal problem (Giambiagi 2021), which was exacerbated by the global recession from 2007 to 2010, triggered by the financial crisis originating in the US subprime mortgage markets (Tourinho and O.Brum 2020). This fiscal issue is evident in the acceleration of gross public debt growth. After remaining relatively stable at around 60% from 2007 to 2013, the debt-to-GDP ratio resumed its upward trajectory, reaching 88.59% in 2020. The increase in fiscal deficits and public debt, linked to expansionary fiscal policies during aggregate demand downturns associated with crises, has also sparked discussions about financial markets’ perceptions of fiscal sustainability.

Additionally, in 2015, Brazil entered one of the most severe economic recessions in its history (e.g., Lisboa and Pessôa 2019; Manoel et al. 2024), leading to deteriorating fiscal results and a downgrade to speculative grade status. Between 2014 and 2017, the country experienced unprecedented fiscal deterioration due to a combination of factors. These included a lack of fiscal control, ensuing political instability, and the necessary measures taken by the government to address the issues. These elements primarily contributed to the economic recession of 2014–2016.

Determining whether the economy is in a state of crisis is inherently challenging. In the Brazilian case, The Business Cycle Dating Committee (CODACE) at Fundação Getulio Vargas (FGV) has been utilizing a methodology akin to that of the US National Bureau of Economic Research in order to identify and date recessions in Brazil since 19801. Also, the authors in Gomes et al. (2024) study the modeling business cycles through Markov-switching models in the context of structural breakers and outliers. A substantial body of literature explores the interconnections between economic activity, financial markets, financial stability, and financial crises (e.g., Claessens et al. 2012; Illing and Liu 2003; Monin 2019; Oet et al. 2015; Sandahl et al. 2011; Slingenberg and De Haan 2011). Notably, Balakrishnan et al. (2011) employs the Financial Stress Index (FSI) to investigate financial market turbulence across advanced and Emerging Economies. During the 2008 crisis peak, Emerging Economies experienced significant reactions, evidenced by a sharp rise in the FSI. The author in Moriyama (2010) finds that increased economic stress, as identified by the FSI, may explain about half of the decline in real GDP growth in Emerging Markets. Also, the authors in Soave (2020), who estimate the FSI using the method proposed by Koop and Korobilis (2014), suggest that financial friction plays a crucial role in the business cycles in Emerging Markets.

Empirical studies also show that financial instability and economic downturns are closely related (Baxa et al. 2013; Cardarelli et al. 2011). Researchers have examined the relationship between economic policies and financial stress. For instance, the authors in Li and St-Amant (2010) explore the links between monetary policy, the business cycle, and Canada’s financial sector, concluding that contractionary monetary policy has a more significant impact during severe financial stress. Moreover, Park and Mercado (2014) analyzed FSI data from 25 emerging markets between 1992 and 2012, finding that both regional and non-regional FSIs increased significantly during domestic financial stress.

The authors in Stona et al. (2018), for instance, examine the macroeconomic dynamics during periods of instability in the Brazilian financial market from 2000 to 2015. They introduce the Brazil Financial Stress Index as a proxy for financial stress and assess its interaction with real activity, inflation, and monetary policy. Their findings suggest that an expansionary monetary policy can exacerbate adverse situations. Additionally, the authors in Wichmann and Portugal (2013) investigate the existence of asymmetries in economic policy responses across economic cycles from 2001 to 2010. They suggest that fiscal rules are faster and less asymmetric than other policies, while monetary policy responds more strongly to variations in the output gap.

Since the existing literature on economic policy responses in Brazil is not comprehensive, this paper introduces a novel approach by using the FSI, in accordance with Balakrishnan et al. (2011), as a threshold variable to link financial sector conditions and economic policy responses. We establish two economic states: low-stress (economic growth) and high stress (economic downturn) (Afonso et al. 2018; Alessandri and Mumtaz 2017; Galvão and Owyang 2018). To estimate the parameters governing these regimes, we employ a threshold-VAR (TVAR) method to assess nonlinearities in Brazilian economic policies.

This modeling approach offers significant advantages from a policy perspective as it enables the monitoring of financial stability measures and their regime changes over time. In empirical studies, the primary tools used to capture nonlinearities in fiscal and monetary policy responses are Markov-switching Vector Autoregression (MS-VAR) and Smooth Transition Vector Autoregression (STVAR) models (Evgenidis and Tsagkanos 2017; Li and St-Amant 2010). Regime-switching models typically impose endogenous switches, whereas TVAR models treat the threshold variable as exogenous. This allows for the study of regime switches that result from shocks to other variables within the system (Ferraresi et al. 2015). Another advantage of TVARs is their simplicity in estimation: they are nonlinear multivariate systems of equations that model nonlinearity additively and can be estimated through ordinary least squares (OLS). Once estimated, the state-dependent dynamics of TVARs allow for nonlinear and asymmetric impulse response functions.

We begin by estimating a TVAR model without decomposing fiscal policy into rule and impulse components (mainstream). Following this, we explore five specifications to decompose the fiscal policy, with each specification constituting a separate TVAR exercise. The results indicate that Brazil’s fiscal policy is predominantly procyclical in impulse throughout both regimes, which suggests asymmetry in this component. In contrast, the rule was countercyclical in most specifications and both regimes. Monetary policy exhibited mixed signals across specifications and regimes, resulting in no definitive conclusions.

The outline of the paper is as follows: Section 2 and Section 3 present the methods for filtering impulse fiscal and the TVAR, respectively. Section 4 introduces the Financial Stress Index. Section 5 presents the dataset and our empirical findings, and lastly, Section 6 concludes.

2. Methods for Filtering Impulse Fiscal Policy

When analyzing the path of economic policy, whether fiscal or monetary, it is important to keep in mind that it has automatic and discretionary components (Ilzetzki 2011; Talvi and Vegh 2005; Tornell and Lane 1999). These components can present different paths, so it is possible that procyclicity is present in only one of the components. For example, there is a possibility that the rule component is countercyclical and the discretionary component is procyclical.

The definition of the rule says that the balance increases (decreases) when the output gap rises (lowers). The fiscal impulse can have a greater degree of asymmetry, predominantly countercyclical in the financial stress regime and procyclical in regimes without stress monetary policy can have a countercyclical response during regimes with stress (Balassone et al. 2010; Hercowitz and Strawczynski 2004; Sorensen et al. 2001). The central bank can be more tolerant of the economy’s heating during periods without financial stress, accepting a little more inflation.

According to Woodford (2003), in economies that adopt an inflation-targeting regime, the real interest rate gap is a measure of the stance of monetary policy. On the other hand, there is no consensus in the literature on a measure for the fiscal policy stance. In the absence of a consensual definition, the variation in the structural primary balance as a percentage of GDP, also called fiscal impulse, is generally used as an indicator of the fiscal policy stance (Vitek 2023).

The literature suggests several approaches to calculating the fiscal impulse. Among them, the most frequently cited are as follows: $(1)$ International Monetary Fund $(\mathrm{IMF})$; $(2)$ The Organization for Economic Cooperation and Development $(\mathrm{OECD})$; $(3)$ The Dutch approach, $\mathrm{Dutch}$. Specifically, the $\mathrm{IMF}$ defines the cyclically adjusted fiscal stance as follows:

$$\begin{array}{c}\hfill {\mathrm{FS}}_{\mathrm{IMF}}=\left(G_t-{\displaystyle \frac{G_0}{Y_0^P}}{Y}_t^P\right)-\left(T_t-{\displaystyle \frac{T_0}{Y_0^P}}{Y}_t\right).\end{array}$$

(1)

Therefore, the fiscal impulse measure defined by the International Monetary Fund ($\mathrm{IMF}$) can be expressed as follows:

$$\begin{array}{c}\hfill {\mathrm{FI}}_{\mathrm{IMF}}=\Delta {\mathrm{FS}}_{\mathrm{IMF}}=\left(\Delta G-{\displaystyle \frac{G_0}{Y_0^P}}\Delta Y^P\right)-\left(\Delta T-{\displaystyle \frac{T_0}{Y_0^P}}\Delta Y\right).\end{array}$$

(2)

where G is the government spending, T is the government revenues, Y and $Y^P$ refers to actual and potential $\mathrm{GDP}$, respectively. The subscripts 0 refers to the base year and t the current period.

The $\mathrm{OECD}$ approach calculates cyclically adjusted government revenues and expenditures as follows:

$$\begin{array}{c}\hfill {\mathrm{T}}_{\mathrm{ADJ}}=\left[T-{\eta }_{\mathrm{T}}{\displaystyle \frac{T_{t-1}}{Y_{t-1}}}\left(Y_t-Y^P\right)\right],\end{array}$$

(3)

$$\begin{array}{c}\hfill {\mathrm{G}}_{\mathrm{ADJ}}=\left[G-{\eta }_{\mathrm{G}}{\displaystyle \frac{G_{t-1}}{Y_{t-1}}}\left(U_t-U^P\right)\right],\end{array}$$

(4)

where $T_{\mathrm{ADJ}}$ and $G_{\mathrm{ADJ}}$ is the adjusted government budgetary income and spending, respectively. $U_t$ refers to the unemployment rate, while $U^P$ represents the natural rate of unemployment, which occurs when the economy is operating at its potential2. ${\eta }_{\mathrm{T}}$ and ${\eta }_{\mathrm{G}}$ are the elasticity of government expenditure and revenues relative to $\mathrm{GDP}$, and the subscript $t-1$ refers to the previous period. Thus, the $\mathrm{OECD}$ fiscal impulse is defined as the change in the cycle-adjusted balance:

$$\begin{array}{c}\hfill {\mathrm{FI}}_{\mathrm{OECD}}=\Delta {\mathrm{G}}_{\mathrm{ADJ}}-\Delta {\mathrm{T}}_{\mathrm{ADJ}}.\end{array}$$

(5)

The Dutch method ($\mathrm{Dutch}$) for calculating the fiscal impulse is given by the following:

$$\begin{array}{cc}\hfill {\mathrm{FI}}_{\mathrm{Dutch}}& \hfill =\left(\Delta G-{\displaystyle \frac{\Delta Y^P}{Y_{t-1}^P}}{G}_{t-1}\right)-\left(\Delta T-{\displaystyle \frac{\Delta Y}{Y_{t-1}}}{T}_{t-1}\right).\hfill \end{array}$$

(6)

The $\mathrm{IMF}$ approach calculates the fiscal impulse using a reference year in which the real $\mathrm{GDP}$ is close to potential (the output gap is close to zero). The $\mathrm{OECD}$ method requires the calculation of the elasticities of government revenues and expenditures, which, in the case of the $\mathrm{IMF}$ method, are implicitly considered to be unitary. The Dutch approach is similar to that of the $\mathrm{IMF}$, with the only difference being the choice of reference year, as it uses the previous year as its basis.

In addition to the methods previously presented for measuring the fiscal impulse, two regression-based approaches are also considered: one proposed by the IMF and another estimated using the Kalman filter. Specifically, the regression-based fiscal impulse measure is calculated as the difference between a hypothetical government primary balance, assuming no changes in economic conditions, in period t, and the actual government primary balance outcome in $t-1$ (IMF 2009). The change in the government’s primary balance compared to the previous period is decomposed as follows:

$$\begin{array}{cc}\hfill \Delta B_t& =B\left(P_t,E_t\right)-B\left(P_{t-1},E_{t-1}\right)\hfill \\ \hfill & =\left[B\left(P_t,E_t\right)-B\left(P_t,E_{t-1}\right)\right]+\left[B\left(P_t,E_{t-1}\right)-B\left(P_{t-1},E_{t-1}\right)\right],\hfill \\ \hfill & =\Delta B_t^E+\Delta B_t^P,\hfill \end{array}$$

(7)

where the term $B\left(P_t,E_{t-1}\right)$ refers to the primary balance that would occur under the policies of period t, $P_t$, and the economic conditions of $t-1$, $E_{t-1}$. Thus, the variation in the primary balance can be decomposed into two components: one due to changes in economic conditions and the other resulting from changes in discretionary policies.

Assuming that $\mathrm{GDP}$ growth is a proxy for economic conditions, the following equations are estimated:

$$\begin{array}{cc}\hfill T_t& \hfill ={\alpha }_{\mathrm{T}}+{\beta }_{\mathrm{T}}·g_t+{\gamma }_{\mathrm{T}}·t_t+u_t\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill G_t& \hfill ={\alpha }_{\mathrm{G}}+{\beta }_{\mathrm{G}}·g_t+{\gamma }_{\mathrm{G}}·t_t+e_t,\hfill \end{array}$$

(9)

where T is the government’s current revenue as a percentage of $\mathrm{GDP}$, G is the government’s expenditure as a percentage of $\mathrm{GDP}$, $g_t$ is the real growth of $\mathrm{GDP}$, $t_t$ is a time trend, and $u_t$ and $e_t$ are error terms. With this, it is possible to estimate the adjusted revenue and expenditure that would occur if economic growth remained at the same level as in the previous period:

$$\begin{array}{cc}\hfill T_t^{\mathrm{ADJ}}& \hfill ={\widehat{\alpha }}_{\mathrm{T}}+{\widehat{\beta }}_{\mathrm{T}}·g_{t-1}+{\widehat{\gamma }}_{\mathrm{T}}·t_t+{\widehat{u}}_t\hfill \\ \hfill G_t^{\mathrm{ADJ}}& \hfill ={\widehat{\alpha }}_{\mathrm{G}}+{\widehat{\beta }}_{\mathrm{G}}·g_{t-1}+{\widehat{\gamma }}_{\mathrm{G}}·t_t+{\widehat{e}}_t.\hfill \end{array}$$

Thus, the primary balance that would have occurred in period t if the growth rate had been the same as in $t-1$ can be calculated. The fiscal impulse measure is obtained by the difference between the adjusted primary balance in period t and the actual primary balance in $t-1$.

$$\begin{array}{cc}\hfill {\mathrm{FI}}_{\mathrm{IMF}2008}& =\left(T_t^{\mathrm{ADJ}}-G_t^{\mathrm{ADJ}}\right)-\left(T_{t-1}-G_{t-1}\right)\hfill \\ \hfill & =\left({\widehat{\gamma }}_{\mathrm{T}}-{\widehat{\gamma }}_{\mathrm{G}}\right)+\left({\widehat{u}}_t-{\widehat{u}}_{t-1}\right)-\left({\widehat{e}}_t-{\widehat{e}}_{t-1}\right).\hfill \end{array}$$

(10)

Another approach involves extracting a time series of the unobservable component for the government’s primary balance response $(\%\mathrm{GDP})$ using the Kalman filter. Considering that fiscal policy consists of the variation in the primary balance, $S_t=B_t-B_{t-1}$, this allows for a state-space representation, enabling the Kalman filter to be used for parameter estimation at each point in time. This representation consists of a measurement equation, which represents the evolution of the series $S_t$ over time, and a state transition equation.

$$\begin{array}{cc}\hfill S_t& \hfill =z_t^{\prime }{\alpha }_t+{\mu }_t\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill {\alpha }_t& \hfill ={\Lambda }_t{\alpha }_{t-1}+{\eta }_t,\hfill \end{array}$$

(12)

where $z_t$ represents the output gap, which measures the difference between an economy’s actual $\mathrm{GDP}$ and its potential $\mathrm{GDP}$. It is a measure of the economy’s current position in the business cycle. Therefore, the fiscal policy component $z_t^{\prime }{\alpha }_t$ depends on the economic cycle. The residual terms ${\mu }_t$ and ${\eta }_t$ are normal with zero mean, variances ${\sigma }_{\mu }^2$ and ${\sigma }_{\eta }^2$, and satisfy $\mathbb{E}\left\{{\mu }_t{\eta }_t\right\}=0$.

Note that, unlike the methodologies previously considered, in the Kalman filter-based approach, the impact of the economic cycle on fiscal policy varies over time. The intuition behind this is that the weight given to fluctuations in the output gap may change over time.

3. Financial Stress Index

An episode of financial stress can be defined as a period of interruption in financial markets’ normal functioning (Hakkio et al. 2009), such as generated by the uncertainties brought the COVID-19. A period of financial stress has at least one of these features: increased uncertainty about the value of fundamental assets (Bakas and Triantafyllou 2020; Zhang et al. 2020), increased uncertainty about other investors’ behavior (Bogdan et al. 2021), increased information asymmetry between lenders and borrowers, less willingness to hold risky assets, decreased desire to keep assets less liquid (flight to liquidity), see Davig et al. (2010) for detailed descriptions.

Balakrishnan et al. (2011) developed an index of financial stress for emerging markets based on the existing index of Cardarelli et al. (2009) for developed countries. This index is composed of five variables, namely: “banking sector beta”, stock market returns, stock market volatility, sovereign debt spreads, and exchange market pressure index $\mathrm{EMPI}$. The ${\beta }_t$ of the banking sector is obtained as follows:

$${\beta }_{i,t}={\displaystyle \frac{cov(r_{i,t}^{\mathrm{M}},r_{i,t}^{\mathrm{B}})}{{\sigma }_{\mathrm{M}}^2}},$$

(13)

where $r_t^{\mathrm{M}}$ represents the annual rates of return of the general stock market and $r_t^{\mathrm{B}}$ the rates of return of the shares of companies in the banking sector, the covariance and variance were calculated based on a 12-month moving window. When ${\beta }_t>1$, it is clear that the banking sector presents greater volatility than the rest of the market3. The return of the stock market consists of the year-on-year change in the stock index multiplied by $-1$. Thus, a decline in stock prices implies an increase in stock market stress.

The third variable is the volatility of the stock market. Higher volatility in the stock market can cause an increase in uncertainty and cause an increase in financial stress. The authors in Balakrishnan et al. (2011) estimated such volatility using a $\mathrm{GARCH}$ specification (1,1) for an auto-regressive process variance with 12 lags. However, we use the Exponentially Weighted Moving Average $(\mathrm{EWMA})$ volatility models, considering the six-month moving average of the square of the stock index’s monthly growth rate.

The fourth variable is the sovereign debt spreads. It is defined by the $\mathrm{EMBI}+$ (Emerging Market Bond Index Plus) and is a proxy for country risk. An increase in $\mathrm{EMBI}+$ implies a perception, on the part of the market, that investing in a particular economy has become riskier, which, in turn, can lead to an increase in financial stress. Lastly, the $\mathrm{EMPI}$ captures depreciation of exchange rate and declines in international reserves, and is defined for country i in month t as follows:

$${\mathrm{EMPI}}_{i,t}={\displaystyle \frac{\left(\Delta e_{i,t}-{\mu }_{i,\Delta e}\right)}{{\sigma }_{i,\Delta e}}}-{\displaystyle \frac{\left(\Delta RE{S}_{i,t}-{\mu }_{i,\Delta RES}\right)}{{\sigma }_{i,\Delta RES}}},$$

(14)

where $\Delta e_{i,t}$ and $\Delta RE{S}_{i,t}$ represent changes in the domestic exchange rate and international reserves, respectively, while ${\mu }_{i,\Delta e}$ and ${\sigma }_{i,\Delta RES}$ represent the mean and standard deviation of the variable i. It is clear that the $\mathrm{EMPI}+$ consists of the sum of variables $\Delta e_{i,t}$ and $\Delta RE{S}_{i,t}$ standardized. Domestic currency depreciation as reductions in international reserves pressure the foreign exchange market and, as a result, increases financial stress.

To yield the aggregate Financial Stress Index, we standardized the five components, summed them up, and computed the moving average of six months:

$$FS{I}_t={\beta }_t+SM{R}_t+SM{V}_t+EMB{I}_t+EMP{I}_t.$$

(15)

The next section introduces the threshold-VAR methods and Nonlinear Impulse Response Functions.

4. Threshold-VAR and Nonlinear Impulse Response Functions

In order to investigate the potential presence of nonlinearities in the responses of fiscal and monetary policies, we consider TVAR models with two regimes. The threshold vector autoregression ($\mathrm{TVAR}$4) methodology is a vector autoregression extension that allows the capture of nonlinear relationships. The authors in Balke (2000) noted that for $\mathrm{TVAR}$, it is relatively intuitive and straightforward to capture nonlinearities generated, for instance, by changes in regimes and asymmetries. A $\mathrm{TVAR}$ model with two regimes can be represented as follows:

$$Y_t=\left(D^{(1)}+B^{(1)}(L)Y_{t-1}\right)I_t+\left(D^{(2)}+B^{(2)}(L)Y_{t-1}\right)\left(1-I_t\right)+e_t,$$

(16)

where $Y_t$ is the vector of endogenous variables, $B^{(1)}(L)$ and $B^{(2)}(L)$ are lag polynomial matrices, $e_t$ are structural disturbances, and $I_t$ it is an indicator function that assumes the value 1, when the threshold variable $c_t$ (the financial stress index in our case), with d lags is less than the critical threshold value $\tau$, and 0, otherwise. The parameter d is known as the delay parameter. Algebraically, we have the following:

$$I_t=\left\{\begin{array}{c}\hfill 1,\mathrm{when}{c}_{t-d}<\tau \hfill \\ \hfill 0,\mathrm{when}{c}_{t-d}>\tau .\hfill \end{array}\right.$$

(17)

Thus, the model identifies two distinct regimes based on the values of $c_{t-d}$ and $\tau$. Thus, the indicator variable effectively separates the two regimes and allows regimes to switch endogenously.

The Equation (16) can present a nonlinear path throughout the autoregressive system’s complete trajectory. However, by dividing this trajectory into two parts (that is, where it is less than the threshold value and where it is greater than the threshold value), the system has a linear path. However, the TVAR model is linear within each regime, but the changes in the parameters across regimes account for nonlinearities.

Tong (1978) noted there is a possibility that the system space is composed of at least two subspaces. Although such a system is linear in all segments, it will operate in a nonlinear manner if you consider the space as a whole. In autoregressive modeling with threshold effect (TAR), a threshold variable is defined to capture the system’s movement from one space to another, see Tsay (1989).

The asymmetry of the model described by Equations (16) and (17), which is captured by the threshold variable, allows the constants vector to switch between regimes.

The threshold variable $c_t$ can be modeled into the $Y_t$ vector, allowing the regime change to be endogenously determined by the system. Since the TVAR considers all endogenous variables, shocks in any of the vector variables $Y_t$ can, through their impact on the variable, induce a regime change.

4.1. Econometric Specification

We estimated six $\mathrm{TVAR}$ models. They are formed by the ($\Delta ga{p}_t$) product gap variation, inflation (${\pi }_t$), the variation in the nominal interest rate ($\Delta i_t$), and changes in the fiscal policy’s discretion and rule components, that is, the ($i{f}_t$) fiscal impulse and the rule tax ($r{f}_t$).

In addition to the dataset, the cyclical and discretionary components of fiscal policy were in the estimations, as defined by the OECD, IMF (2006), and IMF (2008) methodologies, and by the Dutch versions and Kalman filter method (see Section 2).

The $\mathrm{TVAR}$ model in Equation (18) can be estimated as follows:

$$X_t=\left(A_0^{(1)}+A_0^{(1)}(L)X_{t-1}\right)I_t+\left(A_0^{(2)}+A_1^{(2)}(L)X_{t-1}\right)\left(1-I_t\right)+e_t,$$

(18)

where $X_t$ is the vector of endogenous variables ($\Delta ga{p}_t$,${\pi }_t$,$\Delta i_t$,$i{f}_t$,$r{f}_t$), $A_0^{(s)}$ is the regime vector’s constants $s=\{1,2\}$, $A^{(s)}(L)$ is the coefficients matrix, and $e_t$ is the error vector, as follows:

$$X_t=\left[\begin{array}{c}\Delta ga{p}_t\\ {\pi }_t\\ \Delta i_t\\ i{f}_t\\ r{f}_t\end{array}\right],A_0^{(s)}=\left[\begin{array}{c}{A}_{10}^{(s)}\\ A_{20}^{(s)}\\ A_{30}^{(s)}\\ A_{40}^{(s)}\\ A_{50}^{(s)}\end{array}\right],A^{(s)}(L)=\left[\begin{array}{cccc}{A}_{11}(L)& A_{12}(L)& \cdots & A_{15}(L)\\ A_{21}(L)& A_{22}(L)& \cdots & A_{25}(L)\\ ⋮& ⋮& \ddots & ⋮\\ A_{31}(L)& A_{32}(L)& \cdots & A_{35}(L)\end{array}\right],e_t=\left[\begin{array}{c}{e}_{1t}\\ e_{2t}\\ e_{3t}\\ e_{4t}\\ e_{5t}\end{array}\right].$$

(19)

The indicator function $I_t$ takes a value of 1 when the economy is under a stress regime in the financial markets and 0 otherwise. $I_t$ is similar to Equation (17):

$$I_t=\left\{\begin{array}{c}\hfill 1,\mathrm{when}fs{i}_{t-d}>\tau \hfill \\ \hfill 0,\mathrm{when}fs{i}_{t-d}\le \tau .\hfill \end{array}\right.$$

(20)

4.2. Nonlinear Impulse Response Functions

Once the estimation of $\mathrm{TVAR}$ is accomplished, it is possible to evaluate whether or not the economic dynamics differ across regimes. In standard linear VARs, the response to a shock is computed assuming that a shock only hits the economy at a particular point in time but neither before nor during the forecasting horizon. Linear VARs are thus history-independent, and reactions to shocks are strictly proportional to the shock itself. However, these convenient properties do not hold within the class of nonlinear models, so Koop et al. (1996) developed a computation of generalized impulse response functions (GIRF).

In threshold-VARs, the reaction of an endogenous variable to a shock depends on the history, the state of the economy, the size of the shock under analysis at time 0, and the size and the sign of all the shocks hitting the economy within the period of interest. The GIRFs approach relies on the simulation of data depending on which regime the system is in at the time the shock hits the economy (the history ${\Omega }_{t-1}$ up to point t). The advantage of GIRFs is not only that it allows for the analysis of regime-dependent responses, but also that the effects of shocks of different sizes and directions can be analyzed. Due to this history and shock dependence, GIRFs lend themselves as an appropriate framework to explore the above-mentioned dimensions of nonlinearity such as regime dependencies, asymmetries (positive vs. negative shocks), and shock nonlinearity (small vs. large shocks).

$$\begin{array}{c}\hfill GIRF=E\left[X_{t+m}\mid {\epsilon }_t,{\epsilon }_{t+1}=0,\dots ,{\epsilon }_{t+m}=0,{\Omega }_{t-1}\right]-\\ \hfill E\left[X_{t+m}\mid {\epsilon }_t=0,{\epsilon }_{t+1}=0,\dots ,{\epsilon }_{t+m}=0,{\Omega }_{t-1}\right],\end{array}$$

(21)

where $X_{t+m}$ is a vector of variables at horizon k, ${\Omega }_{t-1}$ is the information set available before the time of shock t. This implies that there is no restriction regarding the symmetry of the shocks in terms of their sizes because the effects of a ${\epsilon }_t$ shock depend on the magnitude of the current and subsequent shocks. Moreover, in the high stress regime, the size of the fiscal shock matters since a small shock is less likely to induce a change in the regime. Likewise, the impulse responses depend also on the entire history of the variables that affect the persistence of the different regimes. Therefore, to get complete information about the dynamics of the model, the impulse responses have to be simulated for various sizes and the signs of the shocks. The algorithm proceeds as follows.

The general idea is to simulate the model for any possible starting point over the time horizon of interest by feeding the system with bootstrapped shocks and repeating the exercise by adding a new shock of a specific size (1 or 2 times the standard deviation of the fundamental shock in the linear model). The procedure is done hundreds of times with a newly generated series of bootstrapped residuals. Finally, the responses to shocks specific to a particular regime are recovered by averaging the simulation results.

5. Data and Empirical Results

5.1. Data

We employ Brazilian monthly data for the period between January 2003 throughout July 2024. We obtained most of the series through the Time Series Management System of the Central Bank of Brazil (BACEN)5. The variables and their respective sources are specified below:

• Inflation rate ($\pi$): represented by the Extended National Consumer Price Index (IPCA) is the reference for the Brazilian inflation-targeting system, measured in monthly variation and calculated by The Brazilian Institute of Geography and Statistics (IBGE) (BACEN code: 433).
• Unemployment rate (U): We use the rate estimated by Alves et al. (2015) and updated by BACEN in the Inflation Report Statistical Annexes6.
• Domestic product (y): We use the GDP accumulated over 12 months, in constant values from July 2024, adjusted using the IPCA. (BACEN code: 4380).
• Domestic interest rate (i) represented by the annualized Over-Selic rate accumulated in the month, released by the Central Bank (BACEN code: 4189).
• Government revenue (T) consists of total federal government revenue over 12 months, in constant values from July 2024, adjusted using the IPCA (BACEN code: 7544).
• Government spending (G) equivalent to the total federal government expenditure over 12 months, in constant values from July 2024, adjusted using the IPCA (BACEN code: 7547).
• Primary surplus (B) represented by the primary result of the central government over 12 months, in constant values from July 2024, adjusted using the IPCA7.
• EWZ: 12 Months return to measure the performance of the domestic capital market.
• MSCI Financial Brazil: 12 Months return to measure companies’ performance in financial sector.
• USD-BRL Exchange rate: average quotation of the US dollar (sale) published by the Central Bank (BACEN code: 3698).
• International reserves: consist of international funds under the liquidity concept (in USD million), published by the Central Bank (BACEN code: 3546).
• The $(\mathrm{EMBI}+)$: measured in base points and released by JPMorgan.

5.2. Empirical Findings

We present the results of the benchmark $\mathrm{TVAR}$ model (henceforth mainstream) and five $\mathrm{TVAR}$ models that include the fiscal impulse methods—OECD, IMF (2006), Dutch, IMF (2008), and Kalman filter. These methods are described in Section 2. Our results are from 2003 January through July 2024, a time interval that includes data related to COVID-19. Figure 1 presents the FSI, the threshold variable: values above zero are related to a high stress state and below zero are regarded as a low stress regime. Shaded ranges are relative to FSI periods above zero. In these cases, we consider high stress Regime or economic downturn. One can see eleven periods of financial stress, the last of which was due to COVID-19.

According to the threshold variable, we have 61.5% of observations in the low stress Regime and 38.5% in the high stress Regime.

The FSI highlights specific periods of stress: When Luiz Inácio Lula da Silva assumed the presidency of Brazil in 2003, the country was facing uncertainty in economic policies. The 2008 financial crisis was triggered by the collapse of the US housing market, leading to the bankruptcy of Lehman Brothers and a global recession known as the Great Recession. In 2015, the Brazilian economy encountered significant economic challenges. Lastly, in 2020, the COVID-19 pandemic caused a sudden halt in economic activities, resulting in a global recession.

To perform the TVAR estimations, we calculate the first difference of the variables in the vector $X_t$, Equation (19). Also, we performe stationarity tests, lag selection, and lineary tests, see results in Appendix B.

Stationarity tests are used to determine whether a time series is stationary. A time series is stationary when its statistical properties, like mean and variance, remain constant over time. Identifying stationarity is crucial because many time series analysis and modeling methods, such as ARIMA, VAR, and TVAR models, assume the series is stationary. If a series is non-stationary, the relationships between variables may be unstable over time, making accurate forecasting and analysis challenging. Common stationarity tests include the Augmented Dickey-Fuller (ADF) test, the Phillips-Perron (PP) test, and the KPSS (Kwiatkowski-Phillips-Schmidt-Shin) test.

We perform these tests in the time series used in the models and show the results in

Table A1. Stationarity tests.

Time Series	$\mathbf{ADF}$	$\mathbf{KPSS}(4\mathbf{L})$	$\mathbf{KPSS}(12\mathbf{L})$	$\mathbf{PP}(4\mathbf{L})$	$\mathbf{PP}(12\mathbf{L})$
Output Gap	−5.023	0.042	0.034	−6.486	−6.351
IPCA	−4.884	0.080	0.075	−8.442	−8.464
SELIC	−5.416	0.189	0.140	−6.890	−7.292
Balance	−5.185	2.544	1.119	−8.321	−8.085
Impulse OECD	−4.940	0.033	0.033	−15.23	−15.22
Impulse IMF (2006)	−4.754	0.041	0.040	−10.22	−10.09
Impulse Dutch	−4.984	0.120	0.107	−15.28	−15.43
Impulse IMF (2008)	−4.704	0.034	0.034	−14.05	−14.02
Impulse Kalman	−6.280	0.052	0.060	−15.93	−16.14

Note: This table reports the stationarity tests of time series used in our models until now. The tests are Augmented Dickey–Fuller test $(\mathrm{ADF})$, Kwiatkowski–Phillips–Schmidt–Shin tests $(\mathrm{KPSS})$, and Phillips-Perron tests $(\mathrm{PP})$. All entries are least 90% of statistical significance. The variables $\mathrm{IPCA}$, $\mathrm{SELIC}$, $\mathrm{Balance}$, and $\mathrm{FSI}$ represent the inflation rate, the realized interest rate, the primary surplus, and the Financial Stress Index, respectively. The Output gap, interest rate, and Balance are in first difference.

reports the stationarity. All entries are at least 10% of statistical significance. We also tested the presence of nonlinearities in the six specifications defined in Section 2 and Section 4. In

Table A2. TVAR lag selection and LR Linearity Tests.

Panel A: TVAR Lag Selection
	Lags	Mainstream	OECD	IMF (2006)	Dutch	IMF (2008)	Kalman
	1	−14,712.6	−17,585.8	−18,177.6	−17,888.4	−19,494.5	−18,233.7
	2	−14,588.9	−17,384.7	−17,947.5	−17,744.1	−19,868.3	−18,027.0
Panel B: LR Linearity Tests
	$\mathrm{LR}$ Test	52.765	62.58	72.82	60.04	81.76	64.18
	p-value	3.7 × ${10}^{-13}$	2.5 × ${10}^{-15}$	1.4 × ${10}^{-17}$	9.2 × ${10}^{-15}$	1.5 × ${10}^{-19}$	1.1 × ${10}^{-15}$

Note: Panel (A) reports the $\mathrm{TVAR}$ lag selection based on Bayesian information criterion $(\mathrm{BIC})$, in which bold entries represent the chosen model. Panel (B) reports LR Linearity Tests. The null hypothesis is of model linearity.

(Panel A), we present the results of Bayesian information criteria to select the $\mathrm{TVAR}$ lags. Also, a formal test was performed to confirm the nonlinearity of fiscal and monetary responses. The $\mathrm{LR}$ test shown in Table A2 (Panel B) indicated that modeling with regime-switching is the most appropriate, as the null hypothesis of linearity was rejected. This result may justify the use of the $\mathrm{TVAR}$ model. In general, stationarity tests show that all variables are stationary, the TVAR lag selection indicates 1 lag as optimal for models, and LR Linearity Tests reject model linearity for all setups. The estimated parameter results are presented in Appendix B.

When we observe positive signs for parameters between variables from $t-1$ to t, it indicates that the relationship between these variables moves in the same direction. Conversely, a negative parameter in a low-stress regime might remain negative in a high stress regime, suggesting that the variable’s response varies with economic conditions. For instance, the parameter governing the relationship between the output gap (${\mathrm{Gap}}_{t-1}$) and (${\mathrm{Impulse}}_t$) being negative in low stress regime suggests that fiscal policy might be procyclical.

In the TVAR mainstream model, during the low stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly impacts the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.254. In the high stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly affects the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.452, see

Table A3. TVAR mainstream.

	Low Stress Regime (0)					High Stress Regime (1)
	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$
${\mathrm{Gap}}_t$	$\mathbf{0.525}$	$0.022$	$0.040$	$\mathbf{0.115}$	$-0.011$	$\mathbf{0.662}$	$\mathbf{0.063}$	$0.023$	$0.100$	$0.008$
	$0.08$	$0.04$	$0.05$	$0.05$	$0.01$	$0.07$	$0.04$	$0.04$	$0.06$	$0.01$
${\mathrm{IPCA}}_t$	−0.569	$\mathbf{0.444}$	$0.140$	$0.159$	$-0.037$	−0.302	$\mathbf{0.539}$	$\mathbf{0.302}$	$0.033$	$-0.027$
	$0.15$	$0.08$	$0.10$	$0.10$	$0.03$	$0.14$	$0.07$	$0.09$	$0.12$	$0.02$
${\mathrm{SELIC}}_t$	$-0.009$	$\mathbf{0.104}$	$\mathbf{0.749}$	$0.066$	$-0.001$	$0.102$	$\mathbf{0.104}$	$\mathbf{0.710}$	−0.046	−0.056
	$0.09$	$0.05$	$0.06$	$0.06$	$0.02$	$0.09$	$0.04$	$0.05$	$0.07$	$0.01$
${\mathrm{Balance}}_t$	$\mathbf{0.254}$	$0.091$	$\mathbf{0.131}$	$\mathbf{0.217}$	$0.006$	$\mathbf{0.452}$	$\mathbf{0.125}$	$0.001$	$\mathbf{0.513}$	$-0.007$
	$0.11$	$0.06$	$0.07$	$0.08$	$0.02$	$0.10$	$0.05$	$0.06$	$0.08$	$0.01$
${\mathrm{FSI}}_t$	$0.132$	$-0.062$	$\mathbf{0.207}$	$-0.178$	$\mathbf{0.983}$	−0.361	$0.068$	$\mathbf{0.221}$	$-0.102$	$\mathbf{0.925}$
	$0.18$	$0.08$	$0.11$	$0.12$	$0.03$	$0.16$	$0.08$	$0.10$	$0.13$	$0.02$

Note: This table reports the TVAR mainstream parameters in low stress regime. Entries in bold indicates statistically significant at the $10\%$ level. The variables $\mathrm{GAP}$, $\mathrm{IPCA}$, $\mathrm{SELIC}$, $\mathrm{Balance}$, and $\mathrm{FSI}$ represent the output gap, inflation rate, realized interest rate, primary surplus, and Financial Stress Index, respectively.

. This indicates the countercyclical role of past economic performance in shaping current fiscal outcomes across different stress regimes. However, we find different results with the inclusion of Impulse of fiscal policy.

In the TVAR OECD model, during the low stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly impacts the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.642 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of −0.442. In the high stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly affects the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.926 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of −0.459, see

Table A4. TVAR OECD.

	Low Stress Regime (0)						High Stress Regime (1)
	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$
${\mathrm{GAP}}_t$	$\mathbf{0.441}$	$0.018$	$0.041$	$\mathbf{0.070}$	$\mathbf{0.119}$	$-0.007$	$\mathbf{0.634}$	$\mathbf{0.065}$	$-0.002$	$0.018$	$\mathbf{0.089}$	$0.007$
	$0.088$	$0.040$	$0.050$	$0.039$	$0.044$	$0.013$	$0.086$	$0.038$	$0.048$	$0.036$	$0.049$	$0.010$
${\mathrm{IPCA}}_t$	$-\mathbf{0.738}$	$\mathbf{0.463}$	$0.158$	$-0.010$	$\mathbf{0.253}$	$-0.024$	$-\mathbf{0.293}$	$\mathbf{0.536}$	$\mathbf{0.323}$	$-0.037$	$0.029$	$-0.024$
	$0.169$	$0.077$	$0.096$	$0.075$	$0.085$	$0.026$	$0.165$	$0.073$	$0.093$	$0.069$	$0.094$	$0.020$
${\mathrm{SELIC}}_t$	$-0.047$	$\mathbf{0.089}$	$\mathbf{0.740}$	$\mathbf{0.097}$	$0.040$	$-0.002$	$-0.053$	$\mathbf{0.107}$	$\mathbf{0.740}$	$-0.029$	$0.101$	$-\mathbf{0.039}$
	$0.101$	$0.046$	$0.057$	$0.045$	$0.051$	$0.015$	$0.099$	$0.043$	$0.055$	$0.041$	$0.056$	$0.012$
${\mathrm{Impulse}}_t$	$-\mathbf{0.442}$	$0.066$	$\mathbf{0.115}$	$-0.036$	$\mathbf{0.969}$	$\mathbf{0.040}$	$-\mathbf{0.459}$	$-0.026$	$-0.021$	$0.067$	$\mathbf{1}.\mathbf{063}$	$\mathbf{0.030}$
	$0.121$	$0.055$	$0.068$	$0.053$	$0.060$	$0.018$	$0.118$	$0.052$	$0.066$	$0.049$	$0.067$	$0.014$
${\mathrm{Balance}}_t$	$\mathbf{0.642}$	$0.042$	$0.038$	$0.060$	$\mathbf{0.178}$	$-0.027$	$\mathbf{0.926}$	$\mathbf{0.184}$	$-0.011$	$0.103$	$\mathbf{0.185}$	$-\mathbf{0.033}$
	$0.170$	$0.077$	$0.096$	$0.075$	$0.085$	$0.026$	$0.166$	$0.073$	$0.093$	$0.069$	$0.094$	$0.020$
${\mathrm{FSI}}_t$	$0.251$	$-0.080$	$\mathbf{0.189}$	$-0.004$	$-\mathbf{0.205}$	$\mathbf{0.973}$	$-0.262$	$0.060$	$\mathbf{0.243}$	$-0.042$	$-0.134$	$\mathbf{0.920}$
	$0.201$	$0.091$	$0.114$	$0.089$	$0.101$	$0.030$	$0.196$	$0.086$	$0.110$	$0.082$	$0.112$	$0.024$

Note: This table reports the TVAR mainstream parameters in low stress regime. Entries in bold indicates statistically significant at the $10\%$ level. The variables $\mathrm{GAP}$, $\mathrm{IPCA}$, $\mathrm{SELIC}$, $\mathrm{Balance}$, and $\mathrm{FSI}$ represent the output gap, inflation rate, realized interest rate, primary surplus, and Financial Stress Index, respectively.

. These results suggest an influence of the past output gap on current fiscal outcomes and nonconventional policy measures across different stress regimes.

The results in the TVAR IMF (2006) model also suggest an influence of past output gap on current fiscal outcomes and procyclical measures across different stress regimes, see

Table A5. TVAR IMF 2006.

	Low Stress Regime (0)						High Stress Regime (1)
	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$
${\mathrm{GAP}}_t$	$\mathbf{0.576}$	$0.028$	$0.042$	$-0.094$	$0.014$	$-0.010$	$\mathbf{0.760}$	$\mathbf{0.064}$	$0.018$	$-0.163$	$-0.110$	$0.011$
	$0.105$	$0.040$	$0.051$	$0.135$	$0.156$	$0.014$	$0.105$	$0.038$	$0.047$	$0.175$	$0.203$	$0.011$
${\mathrm{IPCA}}_t$	$-\mathbf{0.446}$	$\mathbf{0.457}$	$0.150$	$-0.176$	$-0.108$	$-0.033$	$-0.031$	$\mathbf{0.525}$	$\mathbf{0.265}$	$-\mathbf{0.566}$	$-0.634$	$-0.011$
	$0.199$	$0.076$	$0.097$	$0.256$	$0.297$	$0.026$	$0.199$	$0.073$	$0.088$	$0.333$	$0.386$	$0.021$
${\mathrm{SELIC}}_t$	$0.097$	$\mathbf{0.107}$	$\mathbf{0.749}$	$-0.213$	$-0.160$	$0.003$	$\mathbf{0.329}$	$\mathbf{0.086}$	$\mathbf{0.681}$	$-\mathbf{0.442}$	$-\mathbf{0.596}$	$-\mathbf{0.041}$
	$0.119$	$0.045$	$0.058$	$0.154$	$0.178$	$0.016$	$0.119$	$0.044$	$0.053$	$0.199$	$0.232$	$0.012$
${\mathrm{Impulse}}_t$	$-0.091$	$-\mathbf{0.089}$	$-0.102$	$0.227$	$0.024$	$0.001$	$-\mathbf{0.737}$	$-0.063$	$0.028$	$\mathbf{1}.\mathbf{224}$	$\mathbf{0.904}$	$-0.014$
	$0.139$	$0.053$	$0.068$	$0.179$	$0.207$	$0.018$	$0.139$	$0.051$	$0.062$	$0.232$	$0.270$	$0.015$
${\mathrm{Balance}}_t$	$\mathbf{0.261}$	$\mathbf{0.117}$	$0.084$	$-0.128$	$0.098$	$0.008$	$\mathbf{0.742}$	$0.069$	$-0.046$	$-\mathbf{0.787}$	$-0.391$	$\mathbf{0.029}$
	$0.124$	$0.047$	$0.060$	$0.159$	$0.184$	$0.016$	$0.124$	$0.046$	$0.055$	$0.207$	$0.240$	$0.013$
${\mathrm{FSI}}_t$	$-0.109$	$-0.082$	$\mathbf{0.189}$	$0.350$	$0.359$	$\mathbf{0.975}$	$-\mathbf{0.663}$	$0.080$	$\mathbf{0.258}$	$0.607$	$0.620$	$\mathbf{0.910}$
	$0.235$	$0.089$	$0.114$	$0.302$	$0.350$	$0.031$	$0.235$	$0.086$	$0.104$	$0.392$	$0.456$	$0.025$

Note: This table reports the TVAR mainstream parameters in low stress regime. Entries in bold indicates statistically significant at the $10\%$ level. The variables $\mathrm{GAP}$, $\mathrm{IPCA}$, $\mathrm{SELIC}$, $\mathrm{Balance}$, and $\mathrm{FSI}$ represent the output gap, inflation rate, realized interest rate, primary surplus, and Financial Stress Index, respectively.

. During the low stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly impacts the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.261 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of −0.091. In the high stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly affects the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.742 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of −0.737.

We find similar results in the TVAR Dutch model as prior TVAR IMF (2006) and OECD, see

Table A6. TVAR Dutch.

	Low Stress Regime (0)						High Stress Regime (1)
	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$
${\mathrm{GAP}}_t$	$\mathbf{0.546}$	$0.028$	$0.043$	$-0.041$	$0.079$	$-0.009$	$\mathbf{0.712}$	$0.062$	$0.010$	$-0.036$	$0.034$	$0.004$
	$0.085$	$0.040$	$0.051$	$0.056$	$0.080$	$0.014$	$0.078$	$0.039$	$0.048$	$0.064$	$0.086$	$0.011$
${\mathrm{IPCA}}_t$	$-\mathbf{0.499}$	$\mathbf{0.458}$	$0.153$	$-0.087$	$0.004$	$-0.032$	$-0.241$	$\mathbf{0.528}$	$\mathbf{0.297}$	$-0.141$	$-0.119$	$-0.016$
	$0.162$	$0.076$	$0.097$	$0.107$	$0.153$	$0.026$	$0.150$	$0.074$	$0.092$	$0.123$	$0.165$	$0.021$
${\mathrm{SELIC}}_t$	$-0.023$	$\mathbf{0.106}$	$\mathbf{0.750}$	$0.046$	$0.103$	$-0.004$	$0.129$	$\mathbf{0.099}$	$\mathbf{0.748}$	$-0.066$	$-0.146$	$-\mathbf{0.039}$
	$0.096$	$0.045$	$0.058$	$0.064$	$0.091$	$0.016$	$0.089$	$0.044$	$0.055$	$0.073$	$0.099$	$0.012$
${\mathrm{Impulse}}_t$	$-\mathbf{0.432}$	$-0.096$	$-0.123$	$\mathbf{0.149}$	$\mathbf{0.831}$	$0.020$	$-\mathbf{0.802}$	$-0.101$	$-0.113$	$\mathbf{0.357}$	$\mathbf{0.739}$	$0.024$
	$0.135$	$0.064$	$0.081$	$0.090$	$0.128$	$0.022$	$0.125$	$0.062$	$0.077$	$0.103$	$0.138$	$0.018$
${\mathrm{Balance}}_t$	$\mathbf{0.182}$	$\mathbf{0.116}$	$0.085$	$0.045$	$\mathbf{0.271}$	$0.003$	$\mathbf{0.422}$	$\mathbf{0.086}$	$0.009$	$-0.011$	$\mathbf{0.456}$	$0.006$
	$0.103$	$0.049$	$0.062$	$0.069$	$0.098$	$0.017$	$0.096$	$0.047$	$0.059$	$0.078$	$0.106$	$0.013$
${\mathrm{FSI}}_t$	$0.044$	$-0.082$	$0.186$	$0.044$	$0.027$	$\mathbf{0.980}$	$-\mathbf{0.469}$	$0.087$	$\mathbf{0.251}$	$\mathbf{0.253}$	$0.151$	$\mathbf{0.913}$
	$0.190$	$0.090$	$0.114$	$0.126$	$0.180$	$0.031$	$0.177$	$0.087$	$0.109$	$0.144$	$0.194$	$0.025$

Note: This table reports the TVAR mainstream parameters in low stress regime. Entries in bold indicates statistically significant at the $10\%$ level. The variables $\mathrm{GAP}$, $\mathrm{IPCA}$, $\mathrm{SELIC}$, $\mathrm{Balance}$, and $\mathrm{FSI}$ represent the output gap, inflation rate, realized interest rate, primary surplus, and Financial Stress Index, respectively.

. During the low stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly impacts the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.182 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of −0.432. In the high stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly affects the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.422 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of −0.802.

The TVAR IMF (2008) model differs from the results of previous models. During the low stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly impacts the balance (${\mathrm{Balance}}_t$) with a coefficient of −0.466 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of 0.628. In the high stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly affects the balance (${\mathrm{Balance}}_t$) with a coefficient of −0.482 and the impulse (${\mathrm{Impulse}}_t$) with a coefficient of 0.883, see

Table A7. TVAR IMF 2008.

	Low Stress Regime (0)						High Stress Regime (1)
	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$
${\mathrm{GAP}}_t$	$\mathbf{0.682}$	$0.063$	$0.016$	$0.055$	$-0.145$	$-0.007$	$\mathbf{0.676}$	$0.059$	$0.010$	$0.081$	$0.109$	$0.004$
	$0.090$	$0.040$	$0.050$	$0.056$	$0.095$	$0.013$	$0.082$	$0.040$	$0.047$	$0.062$	$0.103$	$0.010$
${\mathrm{IPCA}}_t$	$-\mathbf{0.446}$	$\mathbf{0.477}$	$0.133$	$0.061$	$-0.059$	$-0.034$	$-\mathbf{0.443}$	$\mathbf{0.503}$	$\mathbf{0.327}$	$0.113$	$0.313$	$-0.024$
	$0.174$	$0.079$	$0.098$	$0.110$	$0.185$	$0.026$	$0.160$	$0.077$	$0.092$	$0.121$	$0.201$	$0.020$
${\mathrm{SELIC}}_t$	$0.100$	$\mathbf{0.132}$	$\mathbf{0.727}$	$0.048$	$-0.106$	$0.002$	$0.060$	$\mathbf{0.105}$	$\mathbf{0.759}$	$-0.028$	$-0.008$	$-\mathbf{0.044}$
	$0.104$	$0.047$	$0.058$	$0.065$	$0.110$	$0.015$	$0.095$	$0.046$	$0.055$	$0.072$	$0.120$	$0.012$
${\mathrm{Impulse}}_t$	$\mathbf{0.628}$	$-0.004$	$0.106$	$\mathbf{0.181}$	$\mathbf{0.548}$	$0.004$	$\mathbf{0.883}$	$0.013$	$0.020$	$\mathbf{0.423}$	$\mathbf{0.436}$	$-0.010$
	$0.169$	$0.076$	$0.095$	$0.107$	$0.179$	$0.025$	$0.155$	$0.075$	$0.089$	$0.118$	$0.195$	$0.019$
${\mathrm{Balance}}_t$	$-\mathbf{0.466}$	$0.091$	$0.021$	$0.087$	$-0.209$	$-0.010$	$-\mathbf{0.482}$	$0.089$	$0.015$	$0.118$	$0.161$	$0.005$
	$0.133$	$0.060$	$0.074$	$0.083$	$0.140$	$0.019$	$0.121$	$0.059$	$0.070$	$0.092$	$0.153$	$0.015$
${\mathrm{FSI}}_t$	$0.151$	$-0.060$	$0.180$	$-0.094$	$-0.197$	$\mathbf{0.983}$	$-0.273$	$0.093$	$\mathbf{0.212}$	$-0.148$	$-0.295$	$\mathbf{0.925}$
	$0.207$	$0.093$	$0.116$	$0.130$	$0.219$	$0.030$	$0.189$	$0.092$	$0.109$	$0.144$	$0.238$	$0.024$

Note: This table reports the TVAR mainstream parameters in low stress regime. Entries in bold indicates statistically significant at the $10\%$ level. The variables $\mathrm{GAP}$, $\mathrm{IPCA}$, $\mathrm{SELIC}$, $\mathrm{Balance}$, and $\mathrm{FSI}$ represent the output gap, inflation rate, realized interest rate, primary surplus, and Financial Stress Index, respectively.

. Even though it presents results opposite to previous TVAR OECD, IMF (2006), and Dutch models, this one still points to a procyclical behavior in fiscal policy, however in the Balance.

Lastly, TVAR Kaman model differs from all models presented previously, see

Table A8. TVAR Kalman Filter.

	Low Stress Regime (0)						High Stress Regime (1)
	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Gap}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{IPCA}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{SELIC}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Impulse}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{Balance}}_{\mathit{t}-\mathbf{1}}$	${\mathbf{FSI}}_{\mathit{t}-\mathbf{1}}$
${\mathrm{GAP}}_t$	$\mathbf{0.491}$	$0.016$	$0.028$	$0.058$	$\mathbf{0.204}$	$-0.013$	$\mathbf{0.668}$	$0.062$	$0.024$	$0.113$	$0.092$	$0.008$
	$0.087$	$0.040$	$0.052$	$0.077$	$0.099$	$0.013$	$0.090$	$0.038$	$0.045$	$0.117$	$0.087$	$0.010$
${\mathrm{IPCA}}_t$	$-\mathbf{0.606}$	$\mathbf{0.438}$	$0.127$	$0.097$	$0.255$	$-0.039$	$-\mathbf{0.290}$	$\mathbf{0.538}$	$\mathbf{0.302}$	$0.057$	$0.018$	$-0.027$
	$0.167$	$0.077$	$0.099$	$0.147$	$0.190$	$0.026$	$0.172$	$0.073$	$0.086$	$0.224$	$0.168$	$0.018$
${\mathrm{SELIC}}_t$	$-0.096$	$\mathbf{0.089}$	$\mathbf{0.719}$	$-0.080$	$\mathbf{0.291}$	$-0.006$	$\mathbf{0.206}$	$\mathbf{0.094}$	$\mathbf{0.716}$	$0.160$	$-\mathbf{0.176}$	$-\mathbf{0.057}$
	$0.100$	$0.046$	$0.059$	$0.088$	$0.114$	$0.015$	$0.103$	$0.044$	$0.051$	$0.134$	$0.100$	$0.011$
${\mathrm{Impulse}}_t$	$0.080$	$0.027$	$\mathbf{0.114}$	$0.045$	$-\mathbf{0.289}$	$-0.001$	$0.074$	$\mathbf{0.088}$	$-0.018$	$-0.043$	$0.037$	$-0.002$
	$0.086$	$0.040$	$0.051$	$0.076$	$0.098$	$0.013$	$0.089$	$0.038$	$0.044$	$0.116$	$0.087$	$0.009$
${\mathrm{Balance}}_t$	$0.084$	$\mathbf{0.048}$	$-0.015$	$0.019$	$\mathbf{0.743}$	$0.002$	$\mathbf{0.137}$	$\mathbf{0.060}$	$0.006$	$0.078$	$\mathbf{0.778}$	$-0.002$
	$0.062$	$0.029$	$0.037$	$0.055$	$0.071$	$0.010$	$0.064$	$0.027$	$0.032$	$0.084$	$0.063$	$0.007$
${\mathrm{FSI}}_t$	$0.244$	$-0.044$	$\mathbf{0.247}$	$0.010$	$-\mathbf{0.468}$	$\mathbf{0.989}$	$-0.317$	$0.065$	$\mathbf{0.224}$	$-0.015$	$-0.158$	$\mathbf{0.925}$
	$0.196$	$0.090$	$0.117$	$0.172$	$0.223$	$0.030$	$0.202$	$0.086$	$0.101$	$0.263$	$0.197$	$0.022$

Note: This table reports the TVAR mainstream parameters in low stress regime. Entries in bold indicates statistically significant at the $10\%$ level. The variables $\mathrm{GAP}$, $\mathrm{IPCA}$, $\mathrm{SELIC}$, $\mathrm{Balance}$, and $\mathrm{FSI}$ represent the output gap, inflation rate, realized interest rate, primary surplus, and Financial Stress Index, respectively.

. During the low stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) does not significantly impact the balance (${\mathrm{Balance}}_t$) and the impulse (${\mathrm{Impulse}}_t$). In the high stress regime, the output gap (${\mathrm{Gap}}_{t-1}$) significantly affects the balance (${\mathrm{Balance}}_t$) with a coefficient of 0.137.

To make the data analysis more robust, we use generalized impulse response functions (GIRFs) in the TVAR results to understand the nonlinear dynamics between economic variables under different regimes, see Section 4.2. GIRFs allow for the analysis of how positive shocks to the output gap, for instance, affect other variables over time, providing a more direct and flexible interpretation. By applying a positive shock to the output gap, we can record responses in fiscal impulse, fiscal rule, and monetary policy and also obtain confidence intervals. This helps capture the interactions between these variables in both regimes.

To clarify the possible policy sets of results, we have summarized them as follows:

• Low Stress (i.e., Growth) Regime:

  –

  Expected Policy: Countercyclical—Contractionary Policy;

  –

  Nonconventional Policy: Procyclical—Expansionary Policy;

• High Stress (i.e., Downturn) Regime:

  –

  Expected Policy: Countercyclical—Expansionary Policy;

  –

  Nonconventional Policy: Procyclical—Contractionary Policy.

First, we describe the mainstream model in the low stress regime, which, by definition, represents a period of economic growth. Observing the two lower panels of Figure 2, a positive shock to the output gap results in a positive response in the Balance and a negative response in the Selic rate. This indicates that fiscal policy is contractionary (countercyclical), aligning with what is prescribed in the literature, whereas monetary policy (SELIC) is expansionary (procyclical), albeit only slightly different from zero, between approximately 7.5 and 10 months after the shock.

In the high stress regime, characterized by an economic downturn, the results are presented in the two upper panels of Figure 2. Here, applying a positive shock to the output gap also results in a positive response in the Balance. Conversely, a negative shock to the output gap would yield a negative Balance, demonstrating that fiscal policy is expansionary (countercyclical). Regarding monetary policy, applying the same analogy, a negative shock to the output gap results in a negative monetary policy response, suggesting that monetary policy is expansionary (countercyclical). Thus, under both policies, we observe expansionary (countercyclical) measures. Therefore, the mainstream model suggests that fiscal policy is countercyclical in both regimes, while monetary policy is countercyclical only in the high stress regime.

In the OECD model, within the low stress regime (economic growth), we decompose fiscal policy into Balance and Impulse, see Figure 3. The response of Balance to a positive shock in the output gap is statistically positive in the initial periods, suggesting that this component of fiscal policy is contractionary (countercyclical). However, Impulse is statistically negative in the initial periods, suggesting that this component of fiscal policy is expansionary (procyclical). Monetary policy, however, does not show statistically significant signals.

In the high stress regime, a period of economic downturn, monetary policy also does not show signals different from zero. However, the Balance of fiscal policy is positive after a positive shock in the output gap; otherwise, it would be negative after a negative shock in the output gap. Thus, we observe that part of fiscal policy is expansionary during an economic stress, responding in a countercyclical manner. Also analyzing the signals oppositely, the response of Impulse would be positive to a negative shock in the output gap, indicating that it is contractionary during a stress period (procyclical). Therefore, this model suggests that fiscal policy responds with asymmetric forces, with Balance being countercyclical and Impulse being procyclical.

In the IMF (2006) model, as shown in Figure 4, the results suggest the same interpretation as the OECD model in the disaggregations of fiscal policy and in both regimes: in the low stress regime, the response of Balance is contractionary (countercyclical) and Impulse is expansionary (procyclical). In the high stress regime, the response of Balance is expansionary (countercyclical) and Impulse is contractionary (procyclical). On the other hand, monetary policy is significantly expansionary in the high stress regime (countercyclical), but without statistically significant results in the low stress period. Therefore, this model also suggests that fiscal policy responds with asymmetric forces, with Balance being countercyclical and Impulse being procyclical. Also, the Dutch model presents similar results to the IMF (2006) model, see Figure 5. Fiscal policy responds with asymmetric forces, with Balance being countercyclical and Impulse being procyclical.

The model that stands out from the others is the IMF (2008), as shown in Figure 6, as the responses of Balance and Impulse are opposite to those in the Dutch, IMF (2006), and OECD models. In the low stress regime, the response of Balance to a positive shock in the output gap is negative, indicating an expansionary movement (procyclical), and the response of Impulse is positive, suggesting a contractionary movement (countercyclical). In the high stress regime, the response of Balance is contractionary (procyclical), as there would be an increase in Balance in response to a negative shock in the output gap during an economic crisis, while Impulse is expansionary (countercyclical). On the other hand, monetary policy does not show statistically significant signals in either regime. Nonetheless, the IMF (2008) model also suggests that fiscal policy responds with asymmetric forces, with Balance being procyclical and Impulse countercyclical.

Lastly, we have the Kalman model, see Figure 7. In this analysis, the results suggest that only in the high stress regime do we observe statistically significant responses, specifically in the responses of Balance and the SELIC. At this point, both fiscal and monetary policies exhibit expansionary movements during a crisis, meaning they are countercyclical, which aligns with the results of the Dutch and IMF (2006) models.

It is worth noting that only the OECD model takes into account the unemployment rate and the structural unemployment rate, which could make its results more robust. Therefore, the fact that the results of the Dutch and IMF (2006) models are also similar to the OECD model helps to strengthen the interpretation of the presented exercises; that is, fiscal policy responds with asymmetric forces, with Balance being countercyclical and Impulse procyclical. Even the results of the IMF (2009) model also suggest that fiscal policy responds with asymmetric forces in both cycles.

In summary, the mainstream model indicates that fiscal policy is countercyclical in both low stress (growth) and high stress (crisis) regimes, with monetary policy being countercyclical only in high stress. The OECD model decomposes fiscal policy into Balance (countercyclical) and Impulse (procyclical), showing asymmetric responses in both regimes, with monetary policy showing no significant signals. The IMF (2006) model aligns with the OECD model, indicating countercyclical Balance and procyclical Impulse, with monetary policy being expansionary in high stress. The Dutch model produces similar results to the IMF (2006) model. On the contrary, the IMF (2008) model shows opposite responses: Balance is procyclical and Impulse countercyclical in both regimes, with no significant monetary policy signals. The Kalman model reveals statistically significant countercyclical responses for both fiscal and monetary policies in the high stress regime, aligning with the Dutch and IMF (2006) models. The robustness of the OECD model is strengthened by considering unemployment rates, with similar results in the Dutch and IMF (2006) models supporting the interpretation of asymmetric fiscal policy responses.

Also, by using generalized impulse response functions (GIRFs), we capture the nonlinear dynamics and initial statistical significance of fiscal impulse, balance, and monetary policy responses. This comprehensive analysis underscores the importance of considering methodological approaches when interpreting fiscal policy impacts, ensuring robust and context-sensitive economic assessments.

These results are consistent with broader studies such as those by Ilzetzki and Végh (2008), which found overwhelming evidence to support the idea that procyclical fiscal policy in developing countries is indeed a reality and not fiction. The main contributions of our results are twofold. First, we present five methods to disaggregate fiscal policy into rule and impulse, allowing for comparisons among results and creating a scoreboard based on statistical significance. Second, the confidence interval of the generalized impulse response function provides robustness that is absent in Wichmann and Portugal (2013), whose results also suggest asymmetries in fiscal policy.

Our results are in line with Arena and Revilla (2009), which discusses procyclical fiscal policy in Brazil, with evidence from the states. Their results suggest the existence of a procyclical fiscal policy in Brazil at the state level. However, the introduction of the Fiscal Responsibility Law in 2000 helped to reduce spending-side procyclicality in Brazilian states.

Moreover, assuming the hypothesis of procyclical spending is inefficient for smoothing economic cycles, the results from Holland et al. (2020) further support this inefficiency. They argue that while fiscal policy predominantly operated in a countercyclical manner, monetary policy was procyclical. Additionally, They argue that estimates of the government spending multiplier are generally close to zero. While higher multipliers are reported using TVAR and other methods, these are not robust due to specification issues. Therefore, this introduces further inefficiencies in the Brazilian economy.

In general, for economies with procyclical fiscal policy, some suggestions include implementing countercyclical policies, Bova et al. (2014). This involves adopting fiscal policies that counter economic fluctuations by increasing public spending during recessions and reducing it during economic expansions. Maintaining fiscal stability is also crucial, ensuring a balanced budget and avoiding excessive fiscal deficits that could exacerbate economic fluctuations. Additionally, it is important to promote structural reforms that improve the efficiency of the public sector and reduce reliance on procyclical fiscal policies. These measures can help mitigate the negative effects of procyclical fiscal policies and promote a more stable and sustainable economy.

6. Concluding Remarks

This paper examines the responses of fiscal and monetary policies during periods of financial stress in Brazil. Using the Financial Stress Index (FSI) as a threshold variable, the study identifies two states: low-stress (economic growth) and high stress (economic downturn). Findings from various $\mathrm{TVAR}$ models indicate significant asymmetries in fiscal policies. The research covers data from January 2003 to July 2024, including the economic disruption caused by COVID-19, which was marked by significant fiscal interventions aimed at mitigating the economic downturn.

The mainstream model shows countercyclical fiscal policy in both regimes, with monetary policy being countercyclical only in high stress. The OECD model finds asymmetric fiscal responses: Balance is countercyclical and Impulse is procyclical, with no significant monetary signals. The IMF (2006) and Dutch models align with the OECD results. The IMF (2008) model stands out, showing procyclical Balance and countercyclical Impulse, with no significant monetary signals. The Kalman model finds statistically significant countercyclical fiscal and monetary responses in high stress, which is similar to the Dutch and IMF (2006) models. The OECD model’s consideration of unemployment rates adds robustness to its findings, which are supported by similar results in the Dutch and IMF (2006) models.

Therefore, this study underscores the significance of incorporating methodological approaches when analyzing the impacts of fiscal policy, which indicates that the government’s fiscal policy has predominantly exhibited procyclical tendencies in terms of Impulse. This highlights the necessity for more robust and context-sensitive economic assessments to ensure the stability and sustainability of economic policies.