2.1 Central Bank Reaction Function

^{Taylor (1993)} argued that the behavior of the American Central Bank could be described by a simple rule that linked changes in the interest rate to deviations in inflation and output from their potential. In the present article, in particular, the monetary policy rule is forward-looking and will be modified with the inclusion of fiscal policy sentiment, and it can be described as:

or in its estimated form:

where the variables with a circumflex are in the form of deviations from the Hodrick-Prescott (HP) filter; r _t is the nominal interest rate; 𝜋 _t+1 is the inflation rate; y _t is the real output of the economy; s _t is the fiscal policy sentiment; e _t is a shock that captures the non-systematic components in the monetary policy rule; and Γ𝜋=(1−𝜌𝑟)𝑟𝜋,Γ𝑦=(1−𝜌𝑟)𝑟𝑦,Γ𝑠=(1−𝜌𝑟)𝑟𝑠.

The monetary policy rule presented above was estimated using OLS and GMM. According to ^{Silva and Besarria (2018)}, regarding the OLS method, it is noted that it may produce biased and inconsistent estimates in the presence of endogeneity. In this case, GMM is used as an alternative method. It is emphasized that the adequacy of the statistical inference generated by this method is linked to the exogeneity and relevance of the instruments adopted. In other words, the instruments must be orthogonal to the residuals and strongly correlated with the endogenous variables included. Furthermore, the efficiency of the estimators is directly related to the identification analysis of the selection of instrumental variables. To select the set of instruments, the selection criteria described in ^{Andrews (1999)} were used, while the over-identification hypothesis was addressed using the J-test.

Table 1 summarizes the variables, sources, frequency, and main treatments applied before estimation.

Furthermore, for the estimation using the GMM method, we employed a comprehensive set of instruments, including real income, the Selic rate, and inflation expectations, as well as lags of fiscal sentiment and GDP. Additional fiscal variables, such as the primary balance, public debt, public debt cycle, nominal balance expectation, and public debt expectation, were also incorporated to capture broader fiscal conditions and isolate the effect of fiscal communication on the Central Bank's reaction function. Quarterly data spanning from the first quarter of 2003 to the second quarter of 2021 were used in the estimation.

All series were seasonally adjusted prior to estimation to remove short-term fluctuations and align temporal frequency. The GDP and investment series were expressed as deviations from their long-term trends estimated through the Hodrick-Prescott (HP) filter. Inflation was measured as deviations from the inflation target. Fiscal variables, such as the primary balance and public debt, were normalized to represent deviations from their respective averages, while sentiment indices were rescaled to range between -1 and 1. Inflation, nominal balance, and public debt expectations were incorporated as forward-looking indicators, reflecting the anticipatory behavior of economic agents.

2.2 Textual Estimation Procedure

In this section, the methodology for constructing the sentiment indices (5) will be presented. The process was carried out similarly to the work of ^{Jesus and Besarria (2022)}; however, the authors constructed sentiment indices using BCB communications. In this research, the fiscal policy sentiment index was obtained from the texts of the Federal Public Debt Monthly Reports. The publication of these reports began in November 2000 in Portuguese and in March 2003 in English. In the present work, the English version of the report was chosen, primarily because the most notable and widely accepted dictionary used in sentiment analysis was developed in this language, as proposed by ^{Loughran and McDonald (2011)}.

After collecting the debt reports from the National Treasury website through web scraping, several steps were undertaken to process the set of documents to extract as much information as possible from the linguistic corpus, thereby minimizing the loss of information resulting from sample manipulation. Before performing the lexicographic analysis on the documents, a series of transformations were applied to the original text. The text is first divided into a sequence of substrings (tokens), with all characters converted to lowercase letters. Additionally, stop words were removed, as they do not add relevant information to the analysis.

Each S _t aims to capture some of the narrative information in the report at time t, for each document in our sample. This measure transforms thousands of words into a single number. To obtain each fiscal policy sentiment series S _t , we used three approaches: one that measures sentiments using dictionaries with fixed lexicons, another that uses machine learning models to construct a time-variant dictionary, and another that employs unsupervised machine learning.

According to ^{Shapiro, Sudhof, and Wilson (2020)}, there are two general methodologies for quantifying sentiment in text. The first is known as the lexical methodology. This approach relies on predefined lists of words, called lexicons or dictionaries, with each word assigned a score for the emotion of interest. Typically, these scores are simply 1, 0, and -1 for positive, neutral, and negative, but some lexicons include more than three categories. Typical applications of this approach measure the emotional content of a given text corpus based on the prevalence of negative vs. positive words in the corpus. These word-matching methods are called bag-of-words (BOW) methods because the contextual characteristics of each word, such as its order in the text, grammatical class, co-occurrence with other words, and other context-specific features in the text where the word appears, are ignored.

Among this type of method, the dictionary created by ^{Loughran and McDonald (2011)} (hereafter, LM) stands out. The authors developed lists of negative and positive words selected to be appropriate for financial texts. They demonstrate that their dictionaries are superior for classifying economic and financial texts compared to other dictionaries, such as that of ^{Apel and Grimaldi (2012)} and the Harvard Psychosociological Dictionary, which tend to miscategorize neutral words in a financial/economic context (e.g., taxes, costs, capital, expense, liability, risk, surplus, and depreciation). The LM dictionaries contain 2,355 negative words and 354 positive words. Therefore, for constructing the sentiment indices using the fixed-dictionary approach, we used the LM dictionary.

^{Shapiro, Sudhof, and Wilson (2020)} state that the second and more nascent approach employs machine learning (ML) techniques to build complex models that probabilistically predict the sentiment of a given text set. One of the applications of ML models is in the construction of time-variant dictionaries. ^{Lima, Godeiro, and Mohsin (2019)} used this approach to create a time-variant dictionary method.

According to ^{Lima, Godeiro, and Mohsin (2019)}, the assumption of a time-invariant dictionary does not seem realistic in documents that introduce new words over time or if the vocabulary used during periods of recession differs from that used during periods of economic expansion. The authors emphasize that even if the vocabulary were constant over time, the predictive power of certain words might vary; in other words, the relevance of words changes over time. However, the existing literature does not address this effect, and, as a result, the resulting predictors do not reflect the most predictive textual information found in the documents at a given moment. In the current context of the Covid-19 pandemic, the use of a time-variant dictionary is essential, as new terms have become relevant in the communications of monetary and fiscal authorities. Therefore, for constructing sentiment indices using time-variant dictionaries, we employed the approach developed by ^{Lima, Godeiro, and Mohsin (2019)}.

Thus, using the methodology proposed by the authors to construct the time-variant dictionary, we first created a vector of time series, X _t , where each element of the vector shows time series observations of the frequency with which each word (or combination of words) appears in the monthly debt report up to time t. Therefore, this step transforms the words into numerical values without using a pre-specified (fixed) dictionary. This numerical representation is high-dimensional and sparse; thus, dimensionality reduction must be employed. In the second step, we used supervised machine learning to select the most predictive time series (words) 𝑋_𝑡 ^∗⊂X_t. The elastic net model was chosen to perform this step:

where h ≥ 0 is the forecast horizon h > 0 are estimated by minimizing the following objective function:

where W _t is a к x 1 vector of predetermined predictors, such as lags of y _t as well as traditional structured data predictors, and ║ -║ _l1 and ║ -║ _l2 are the l ₁ and l ₂ norms, respectively. After the dimensionality reduction step and the selection of the most predictive time series 𝑋_𝑡 ^∗⊂X_t using the elastic net model above, the set of selected words (X ^* _t ) for each period t is the one with the highest predictive power regarding the variable of interest y _t+h . This set of words is considered our dynamic sentiment dictionary for period t.

To construct the sentiment index, we calculate the aggregate contribution of the words selected in the dynamic dictionary for each monthly debt report. Specifically, the sentiment variable S _t is obtained as a function of the frequency of occurrence of the selected words X ^* _t in the report, weighted by the prediction coefficients (𝜙_h) estimated in the elastic net model. These coefficients capture the statistical relationship between the occurrence of the words and the variation of the variable of interest over time. In the present article, our response variable for constructing the time-variant dictionary will be the General Government Gross Debt (DBGG) as a proportion of GDP.

Finally, both dictionary approaches calculate the sentiment index as the difference between positive and negative words, divided by the sum of positive and negative words, as proposed by ^{Hubert and Labondance (2018)}:

Thus, we obtain the sentiment measure, S, which ranges between -1 and 1.

To enhance the robustness of the analysis, we also constructed a sentiment index using an unsupervised machine learning model, in this case, the Latent Dirichlet Allocation (LDA) model. The LDA model allows the discovery of latent topics within a set of documents. According to ^{Lin and He (2009)}, LDA learns the topic distribution for each document and the word distribution for each topic, where the discovered topics are represented as lists of words with associated probabilities, indicating the importance of each word within the topic. ^{Venugopalan and Gupta (2022)} state that the resulting topics should be interpreted semantically and with sentiment polarities. The semantic analysis of the topics seeks to identify the general themes. Subsequently, the polarity analysis assigns sentiments (positive, negative, neutral) to the topics based on the qualitative analysis of the most representative words for each topic.

According to ^{Lin and He (2009)}, for constructing the sentiment index from the topics of the LDA model, it is necessary to calculate the topic proportions in each document, where each document has a distribution over the topics, indicating the relevance of each topic to the document. Next, it is necessary to assign a sentiment value to each document: Using the topic proportions and the sentiment polarity associated with each topic, a sentiment score is calculated for each document³.

Thus, the present study proposes to construct three sentiment indices:

2.3 DSGE Model

For the present section, we use the base model from the work of ^{Jesus, Besarria, and Maia (2020)}. The modification introduced by this article to that model is the creation of another version of the interest rate rule. Thus, two DSGE models will be estimated. The first is the base model with the traditional interest rate rule, as in the work of Jesus, Besarria, and Maia (2020) (basic model). The second includes a modified interest rate rule with the creation of a fiscal sentiment variable within the model, incorporated into the Taylor rule.

2.3.1 Fiscal Policy

The role of the fiscal authority in the economy is to collect taxes and issue bonds to finance its public investment and spending. The government's tax revenue (T _t ) is composed of taxes levied on household consumption (x ^c ), labor income (x ^l ), and capital income (т ^к ). The government's intertemporal budget constraint establishes that the current level of public debt must equal the present value of future primary surpluses, ensuring fiscal solvency in the long run. In operational terms, the government's flow constraint in each period can be written as:

where SP _t represents the government's real primary surplus; d _t is the real value of public debt . The variable b _t is the total amount of public bonds, b _t = b' _t + Ъ'' _t .

The primary surplus is given by the difference between the government's total revenue and total expenditure during the same period:

where:

Being the government's revenue from household income; the government's revenue from taxing the return on physical capital owned by patient households; the government's revenue obtained from the total household consumption, and consequently, government consumption is also taxed. Public investment (l _g ) is considered an exogenous shock.

The variable that aims to represent fiscal policy sentiment will be defined in the model based on the fiscal environment. In this case, an increase/decrease in government debt induces a negative/positive polarity in the variable that measures the sentiment of the fiscal authority⁴. Therefore, the variable that will measure the net negativity of the authority is given by:

If the difference in public debt is positive/negative, we will have higher/lower net negativity, resulting in a more pessimistic/optimistic fiscal policy sentiment; e _SFt represents a shock arising from abrupt changes in the fiscal environment.

2.3.2 Monetary Policy

The monetary authority adopts an inflation target and sets the interest rate through a rule proposed by ^{Taylor (1993)}. As indicated, two versions of the interest rate rule will be considered. A basic version, where the central bank looks only at the lagged interest rate level and deviations in future developments and GDP, which we will call the "basic rule", while in the second version, we include deviations in inflation expectations at horizon t + p from its steady-state level. We will call this version of the instrument rule the extended version. The basic version can be represented by the following expression:

This rule specifies that the current nominal interest rate depends on an inertial or lagged component ; the deviation of expected inflation from the target set by the monetary authority; the output gap, represented by the deviation of output from its steady-state value; and, finally, an i.i.d. monetary policy shock, e _R , _t . The subscripts p e z are integers that can take any value. The extended version can be represented by:

where S _t is the variable that measures fiscal sentiment.

2.4 Bayesian Estimation

In this section, we discuss our methodology for estimating and evaluating the models. The solution of the DSGE model was obtained through a first-order Taylor approximation of the equilibrium conditions around the non-stochastic steady-state value. Given the model solution as a state-space representation and a vector of observable variables, the models were estimated using Bayesian techniques. Specifically, a Metropolis-Hastings algorithm, which is a Markov Chain Monte Carlo (MCMC) method, was employed to obtain the posterior probability distribution of the parameters. Two independent chains were generated, each consisting of 400,000 draws, using the Metropolis-Hastings algorithm. The average acceptance rate across the two chains was approximately 40%, and convergence was assessed using the methods proposed by ^{Brooks and Gelman (1998)}. The first 180,000 draws were discarded to ensure independence from initial conditions. The statistics of interest were then calculated based on the joint ergodic posterior probability distribution of the structural parameters.

For the estimation, three variables were used for each quarter: real GDP, nominal interest rate, and household consumption. These variables were chosen because they are the most relevant endogenous variables. The variables were used in natural logarithms and seasonally adjusted. The cyclical component of the variables was obtained using the Hodrick-Prescott filter and covers the quarterly period from the first quarter of 2003 to the second quarter of 2021. The model was estimated using Dynare within the Matlab software.

2.5 Calibration and Prior Distributions

Some parameters were fixed during the estimation process, while others were estimated. For the parameters that were kept fixed, we chose to use values from the related literature ^{Christiano and Eichenbaum (1992)}, ^{Lim and McNelis (2008)}, ^{Silva, Paes, and Ospina (2014)}, ^{Cavalcanti et al. (2018)}, ^{Wesselbaum (2017)}. Table 5 in Appendix (A) presents a brief description of these parameters.

For the estimated parameters, we opted to use prior distributions similar to those employed in the related literature. For the parameters indicating the degree of substitution between private consumption and the consumption of public goods and services, μ_𝑝 e μ_𝑖,, we used a prior beta distribution with a mean of 0.50, consistent with the value found for Brazil by ^{Ferreira and Nascimento (2005)}, ^{Santana, Cavalcanti, and Paes (2012)}, and ^{Bezerra et al. (2014) 5}, with a standard deviation of 0.02 for both. For the parameters of the Taylor rule, we used prior distributions and values for the hyperparameters commonly found in the literature (^{Smets and Wouters, 2003}). The parameter governing the central bank's response to price changes, ϕ _π , was set to 1.5, satisfying the Taylor principle. For the coefficient measuring the central bank's response to the output gap, 𝜙_𝑌, we used a prior normal distribution with a mean of 0.125 (^{Carvalho, Silva, and Silva, 2013}).

For the parameter indicating the share of physical capital in the production function, similar to ^{Cavalcanti et al. (2018)}, we adopted a prior normal distribution with a mean of 0.30 and a standard deviation of 0.05. Finally, for all autoregressive parameters, we employed a prior beta distribution with a mean of 0.95 and a standard deviation of 0.02.

3.3 Estimations of the Reaction Function

For the estimation of the monetary policy rule, in addition to the traditional variables (interest rate, inflation gap, and output gap) and sentiment indices, other fiscal and fiscal expectations variables were added. The objective of adding these variables is to try to isolate the effects of fiscal communication in the Central Bank's reaction function. The additional variables are:

Government Primary Balance, Government Nominal Balance, Public Debt, Public Debt Cycle, Primary Balance Expectation, Nominal Balance Expectation, Public Debt Expectation.

Table 2 presents the estimations of the Central Bank's reaction function using OLS and GMM. Columns 2 and 3 show the OLS estimates of the reaction function, while columns 4 and 5 present the reaction function estimates obtained using the GMM method. The first includes the fiscal sentiment indices in the reaction function, while the second restricts the interest rate response to variations in the sentiment indices.

As in the work of ^{Silva and Besarria (2018)}, in general, the results obtained from the estimation of the reaction function, regardless of the method, show a high degree of smoothing in the interest rate dynamics, indicating that the Central Bank makes gradual changes to the interest rate. Regarding the coefficient related to inflation expectations, it is observed that it is statistically significant and greater than one, indicating that the Central Bank satisfies the Taylor principle by increasing the real interest rate in response to deviations in expected inflation.

Regarding the sentiment indices, the OLS and GMM estimates indicate that the SFF variable does not have statistical significance. The SFL variable showed significance only in the OLS model. On the other hand, the SFV sentiment index demonstrated statistical significance in both models, with a positive sign in the models. Thus, when the tone of the National Treasury's communications is optimistic, the Central Bank increases the interest rate, and when the tone is more pessimistic, the monetary authority reduces the interest rate. It is also worth noting that the weight assigned to variations in fiscal policy sentiment was higher than the weight related to inflation expectations.

These results indicate that fiscal policy sentiment significantly affects the conduct of monetary policy, more specifically through the SFV index. It is worth noting that this sentiment index uses public debt as the dependent variable in its construction, while the SFF index relies on a fixed financial dictionary. Therefore, these results make it evident that the fiscal environment (represented by the sentiment index) is a relevant variable in the conduct of monetary policy. Consequently, such results may suggest the possibility of a fiscal dominance scenario. Since the SFV index was constructed based on public debt as the dependent variable, it reflects the market's perception of fiscal sustainability.

If the results show that the SFV significantly influences monetary policy decisions, this may indicate that the central bank is adjusting its policy based on fiscal conditions. In other words, when the SFV reflects fiscal deterioration, the central bank may choose not to raise interest rates, even if inflation is rising, to avoid worsening the government's fiscal situation.

This subordination of monetary policy to fiscal needs is a clear indication of fiscal dominance, where the need to stabilize public finances takes precedence over controlling inflation or other monetary policy goals.

Despite these results, the estimation of simple equations presents some issues. As highlighted by ^{Lubik and Schorfheide (2007)}, ^{Finocchiaro and Heideken (2013)}, and ^{Silva and Besarria (2018)}, these estimations suffer from endogeneity when estimated by OLS and may exhibit bias when estimated by GMM, due to sample size and bias related to the use of stages in two-stage GMM and iterative GMM estimations, which is proportional to the number of moment conditions in instrumental variable models. Moreover, in practice, finding good instruments to implement the GMM method is not trivial. Invalid or weak instruments represent a serious challenge for reliable inference and may compromise the estimates.

3.4 Estimations of DSGE Models

This subsection presents the results of the estimation of the DSGE models. Table 5 (Appendix) shows the mean values, standard deviations, and the corresponding lower (HPD inf) and upper (HPD sup) bounds of the 95% Highest Posterior Density (HPD) credibility interval for the estimated parameters using the Bayesian inference technique for the two types of models estimated.

As found in the work of ^{Silva and Besarria (2018)}, it is observed that the estimated parameters show little variation between the two models, with posterior means very close between the two. The estimation results reveal that Brazilian data provide little information regarding the amount of labor supplied by patient households in the production of intermediate goods. A similar result was identified by ^{Finocchiaro and Heideken (2013)} in their estimations of this parameter for the United Kingdom and Japan, where the posterior mean value was exactly equal to the prior value.

For the parameters defining the maximum borrowing capacity of impatient households and entrepreneurs, the values were lower than the prior mean. These estimates may reflect the fact that households and firms in the country face more restrictive access to credit compared to developed countries.

The parameters for preference and technology shocks were higher than the prior mean, revealing that these shocks are more persistent than initially hypothesized by the prior distribution hyperparameters. ^{Finocchiaro and Heideken (2013)} obtain similar results in their estimations of shock processes for the United States, United Kingdom, and Japan.

Regarding the parameters of the Central Bank's reaction function, the parameter measuring the Central Bank's response to changes in inflation expectations was positive and greater than one, satisfying the Taylor principle. Similarly, the parameter measuring the response to output deviations was positive. Both parameters suggest the behavior of a Central Bank operating under a flexible inflation targeting regime, assigning weight to both inflation and the real side of the economy. Regarding fiscal policy sentiment, the mean of the parameter reflecting the Central Bank's response, ф ₅ , was positive and significant. Therefore, as in the case of the simple equation models, there are indications that the BCB explicitly considered fiscal policy sentiment, i.e., the fiscal environment, in its reaction function during the period analyzed.

According to ^{Silva and Besarria (2018)}, a convenient tool in Bayesian analysis is the use of estimates to compare alternative models. One such method is to use the marginal density of the data associated with each model and compare them, subsequently choosing the model best supported by the data. One way to obtain the marginal density of the data, from the joint posterior distribution, is to use ^{Geweke's (1999)} estimator, the modified harmonic mean estimator. Table 3 presents the values for the marginal density of the data (in log) computed using this estimator.

Based on the model evaluation criteria created by ^{Kass and Raftery (1995)}, we found some evidence in favor of the model that includes fiscal policy sentiment. Therefore, based on the estimations, it can be said that there is evidence, albeit limited, that the BCB explicitly considered fiscal policy behavior in its interest rate decision-making process.

An analysis of the impulse response functions (Appendix B) indicates that the inclusion of fiscal policy sentiment in the reaction function alters the transmission of monetary policy on GDP, household consumption, and labor supply, with the exception of the interest rate. It is also evident that the increase in the interest rate brought typical recessionary effects to the economy, showing that the positive interest rate shock caused a reduction in consumption, labor supply, and aggregate demand. These effects were observed regardless of whether the Central Bank included fiscal policy sentiment in the reaction function or not.

The results obtained from the estimations of the DSGE models, although limited, align with those found in the OLS and GMM model estimations. In other words, the results indicate that fiscal policy sentiment is a relevant variable in the monetary authority's decision-making process regarding the interest rate. Thus, this new investigative approach suggests a high likelihood of the occurrence of the fiscal dominance phenomenon during the analyzed period. These findings converge with those reported in the works of ^{Ázara (2006)}, ^{Junior, Garcia-Cintado, and Junior (2021)}, ^{Ornellas and Portugal (2011)}, and ^{Nobrega, Maia, and Besarria (2020)}.