Disagreement in expectations about public debt, monetary policy credibility and inflation risk premium

Accepted Manuscript Title: Disagreement in expectations about public debt, monetary policy credibility and inflation risk premium Authors: Gabriel Caldas Montes, Alexandre Curi PII: DOI: Reference:

S0148-6195(17)30152-2 http://dx.doi.org/doi:10.1016/j.jeconbus.2017.06.003 JEB 5780

To appear in:

Journal of Economics and Business

Received date: Revised date: Accepted date:

27-9-2016 21-6-2017 23-6-2017

Please cite this article as: Montes, Gabriel Caldas., & Curi, Alexandre., Disagreement in expectations about public debt, monetary policy credibility and inflation risk premium.Journal of Economics and Business http://dx.doi.org/10.1016/j.jeconbus.2017.06.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Disagreement in expectations about public debt, monetary policy credibility and inflation risk premium

Gabriel Caldas Montes a, *, Alexandre Curi b

a

Fluminense Federal University, Department of Economics and National Council for Scientific and Technological Development (CNPq), Brazil. E-mail: [email protected] Address: Rua Alexandre Moura, Bloco F, 8 - São Domingos, Niterói - RJ, 24210-200. b Fluminense Federal University, Department of Economics. Email: [email protected] Address: Rua Alexandre Moura, Bloco F, 8 - São Domingos, Niterói - RJ, 24210-200.

*Corresponding author.

Highlights 

Estimates suggest public debt expectations affect the inflation risk premium in Brazil.



Disagreement in expectations about public debt affects the inflation risk premium.



Monetary policy credibility is able to reduce the inflation risk premium.

Abstract This paper analyzes the determinants of the inflation risk premium in Brazil during the Inflation Targeting period. In particular, different from the existing studies, we analyze the influence of both public debt expectations and disagreement in expectations about public debt on the inflation risk premium, and also the effect of monetary policy credibility on the inflation risk premium. The findings bring two important policy implications. One related to the effect of the expectations formed for the commitment of the government with debt management; and the other related to the effect of the expectations formed for the central bank’s commitment with the Inflation Targeting regime. The results suggest the disagreement in expectations about the public debt affects the inflation risk premium. Furthermore, the findings also suggest the degree of anchorage of inflation expectations in relation to the inflation target (i.e., the monetary policy credibility) affects the inflation risk premium. Keywords: disagreement in expectations; risk premium; interest rate; credibility JEL classification: E31, E43, E52.

1. Introduction The break-even inflation rate (BEIR) – the difference between nominal and real interest rates – is used as an indicator of inflation expectations; but survey data is often considered to give a cleaner measure of inflation expectations (Söderlind, 2011). Thus, as stressed by Söderlind (2011), it is important to understand how the break-even inflation rate differs from survey data on inflation expectations – the so-called “observed break-even deviation”. Based on a modern Fisher equation, Söderlind (2011) and Kajuth and Watzka (2011), for instance, point that such deviation increases due to the inflation risk premium. In the present study, we seek to estimate the effect of several variables on the inflation risk premium for Brazilian bonds over the period from 2005 to 2015, primarily using GMM. We use several variables that are made available by the Brazilian central bank, which allows both for a direct estimate of the inflation premium and several fiscal and monetary variables that might help explain it. The range of variables available for Brazil is broader than is available for a wider range of countries, which is why this study can contribute to the literature. Brazil is an inflation targeting developing country. According to Mishkin (2007), most developing countries presents history of high and persistent inflation rates, history of fiscal imbalances and difficulty in building monetary policy credibility. In this sense, the understanding of the determinants of the inflation risk premium is particularly important for the Brazilian case since Brazil has history of high and persistent inflation rates, history of fiscal imbalances and difficulty in building credibility. Besides, based on the existing relation involving public debt, interest rate and inflation (e.g., Sargent, 1982 and 1983; Barth et al., 1984; Barro, 1989; Elmendorf and Mankiw, 1999; Gale and Orszag, 2002 and 2003; Kinoshita, 2006; Ardagna, Caselli and Lane, 2007; Catão and Terrones, 2005; Sims 2011; Lin and Chu, 2013; Bianchi and Melosi, 2013), and based on the evidence that credibility is important to create a stable macroeconomic environment and to affect interest rates (e.g., de Mendonça, 2007; de Mendonça and de Guimarães e Souza, 2009; Montes, 2013; Montes and Bastos, 2014; Montes and Curi, 2016), we analyze the influence of both public debt expectations and disagreement in expectations about public debt on the inflation risk premium in Brazil, as well as the effect of monetary policy credibility on the inflation risk premium. Therefore, our study differs from other studies related to the determinants of the inflation risk premium since it includes uncertainties related to the fiscal side (such as the disagreement in expectations about public debt), and the credibility of the monetary policy (which is related to the central bank’s ability to make inflation expectations converge to the inflation target). From a policy perspective, the paper focuses on two important aspects. First, the effect of the fiscal side on expectations, and as a consequence, on the inflation risk premium. The rationale is that fiscal deterioration affects expectations formed for the public debt, increasing uncertainty, and creating different judgments over news, or beliefs in models about debt sustainability (which is measured through the disagreement in expectations about net public debt to GDP), and as a consequence, increasing the inflation risk premium. This idea is in accordance with economic theory, which postulates a causal connection between fiscal discipline and inflation (e.g., Leeper, 1991; Sims, 1994 and 2011; Woodford, 1994 and 1995; Loyo, 1999; Catão and Terrones, 2005; Lin and Chu, 2013; Bianchi and Melosi, 2013).

Second, the effect of monetary policy credibility on the inflation risk premium. The idea is that when credibility is higher, a lower inflation risk premium is expected. Empirical studies provide evidence that credibility affects the behavior of both inflation and interest rates (e.g., de Mendonça and de Guimarães e Souza, 2009; Montes, 2013; Montes and Bastos, 2014; Montes and Curi, 2016). The findings presented by these studies reveal that credibility is important to control inflation, to guide inflation expectations and to bring interest rates to lower levels. In a recent study, Montes and Curi (2016) present a theoretical model for assessing the degree of monetary authority’s commitment to price stability. The model reveals that the more credible this commitment, the greater the gain in terms of inflation control, as well as in terms of reducing the volatility of the interest rate. In addition, they present empirical evidence that the credibility of the monetary authority is crucial for the reduction of both inflation and the volatility of the interest rate in Brazil. In this sense, it is possible to argue that credibility represents a key aspect able to affect the inflation risk premium. We construct a time series of the inflation risk premium – such as Söderlind (2011) – based on a modern Fisher equation. We use data on the Brazilian nominal and real interest rates negotiated on BMF&BOVESPA as well as survey data on inflation expectations from financial market experts (reported by the Central Bank of Brazil – CBB). Moreover, using the database of expectations formed by financial market experts provided by the CBB, we calculate the disagreement in expectations about net public debt to GDP, and the monetary policy credibility index proposed by de Mendonça (2007). The period analyzed covers eleven years of the Brazilian IT Regime1 (from 2005M01 to 2015M12). Based on different estimates, we find empirical evidence that the increase of the disagreement in expectations about the public debt to GDP and the deterioration of credibility are able to affect the overall level of the risk premium in Brazil. Hence, the study brings two important policy implications. One related to the effect of the expectations formed for the commitment of the government with debt management; and the other related to the effect of the expectations formed for the central bank’s commitment with the Inflation Targeting regime. It is important to note that the literature on disagreement in expectation is growing, but despite the rich expectation database provided by the CBB, studies for the Brazilian economy are still incipient. The metric itself exposed here – applied in Montes et al. (2016) and Oliveira and Curi (2016) – can open a new frontier for other works with the rich survey database provided by the CBB. The remainder of this paper is organized as follows: the next section presents a literature review; section three addresses the data and the methodology; the fourth section presents the empirical analysis with emphasis on the results obtained through GMM; section five presents a robustness analysis through the estimation of a model using the autoregressive distributed-lag (ARDL) cointegration method; and the last section concludes. 2 – Literature Review Monetary authorities around the world are looking for reliable and appropriate indicators to monitor inflation expectations of market players. One way to monitor these expectations is through securities whose yields are linked to price changes. Thus, inflation 1

Brazilian Inflation Targeting regime began in 1999.

expectations extracted from these securities constitute an important source for monitoring the expectations of market agents. Garcia and van Rixtel (2007) advocate the use of such securities to monitor inflation expectations of market participants.2 For instance, both Ang et al. (2008) and Grishenko et al. (2013) use the market prices of TIPS (Treasury InflationProtected Securities) to obtain expectations, and thus to estimate the inflation risk premium. According to Garcia and van Rixtel (2007), the risk premium is basically the result of two factors: the first is associated with a compensation for the uncertainty related to future inflation, especially in securities with longer maturities, while the second refers to liquidity compensation. Gürkaynak and Wright (2012) argue that the quest for the fundamental macroeconomic explanations of this risk premium is ongoing and inflation uncertainty seems to play a large role in several economic and financial decisions. The risk premium embedded in the interest rate is a topic that has a long tradition in the literature of finance and macroeconomics. Ciccarelli and Garcia (2009) try to figure out the driving factors of the break-even inflation rate and the risk premium in the euro area. Their findings reveal that at short horizons, actual inflation dynamics is the main determinant of BEIRs. At long horizons, financial variables become increasingly relevant, but confidence and cyclical indicators remain important. In turn, Söderlind (2011) looks for proxies that can explain the “observed break-even deviation” in the United States. He argues that this deviation is likely to be driven mainly by inflation risk premium (on the nominal bonds) and liquidity premium (on the real bonds). In particular, his study relates to the literature that addresses the effect of disagreement on the risk premium of the yield curve, treating the disagreement as a “risk factor”. The work of Söderlind (2011) differs from earlier contributions (e.g., Lahiri, Teigland, and Zaporowski, 1988; García and Manzanares, 2007; Wright, 2011), in particular on how to estimate uncertainty from survey data. In addition, based on the studies of Carlstrom and Fuerst (2004) and Shen (2006), Söderlind (2011) incorporates the results of these studies and goes on to check if other factors (inflation uncertainty and inflation disagreement) add explanatory value by capturing the inflation risk premium. Therefore, the “observed break-even deviation” is regressed on measures of inflation uncertainty obtained from survey data, on probability distributions and proxies for real liquidity premium. The results indicate that the regressors are significant and explain a considerable fraction of the movements of the BEIR deviation from market expectation. This leads to significant adjustments of the usual BEIR. It is intuitive to relate the inflation risk premium to inflation uncertainty since the premium is the price the investor pays to go along with inflation uncertainty (Kajuth and Watzka, 2011). Kajuth and Watzka (2011) develop a method to correct break-even inflation rates derived from index-linked bonds for liquidity and inflation risk premia without resorting to survey-based measures. The authors suggest that in a state-space framework the difference between break-even inflation rates and unobserved true inflation expectation is explained by measures of time-varying liquidity and inflation risk premia. Wright (2011) constructs a panel of zero-coupon nominal government bond yields spanning ten industrialized countries3 and nearly two decades. He computes forward rates 2

Garcia and van Rixtel (2007) follow the works of Hetzel (1992), Breedon (1995), Barr and Campbell (1997), Kitamura (1997) and Emmons (2000). 3 The United States, the United Kingdom, Canada, Japan, Germany, Norway, Sweden, Switzerland, Australia, and New Zealand.

and uses two different methods to decompose these forward rates into expected future short-term interest rates and term premiums. He relates these empirical term premia to inflation uncertainty. His findings suggest that term premiums declined internationally over the sample period, with sharp drops in some countries (Australia, Sweden, and the United Kingdom), which apparently reduced inflation uncertainty by making substantial changes in their monetary policy frameworks. However, according to Bauer, Rudebusch and Wu (2014), the small-sample bias in estimates of commonly used affine dynamic term structure models (DTSMs), as in Wright’s paper, has important economic consequences. Conventional estimates lead to term premia that are potentially unreliable and misleading. For many of the countries considered by Wright (2011), term premia simply mirror the trend and cyclical behavior of long-term interest rates, since the bias makes model-based short rate forecasts and hence the expectations component artificially stable at long horizons. In order to capture some other sources of uncertatinties that can affect the inflation risk premium, Buraschi and Whelan (2012) construct proxies of macroeconomic disagreement on both economic variables (such as future real economic activity and inflation) and financial variables (such as future bond prices). They find that disagreement about economic activity helps to explain risk premium, while bond return volatility is mainly linked to disagreement about inflation. Dick et al. (2013) focus on uncertainty about inflation and GDP growth as well as on the effect of disagreement on term risk premium. Their results indicate that forecasters’ term premium expectations are driven by expected macroeconomic conditions as well as the uncertainty of market participants about future output and inflation. In particular, their findings indicate that expectations about risk premia are significantly influenced by expectations about the real macroeconomic activity (such as GDP), while nominal factors (such as inflation expectations) play a minor role. Despite the evidence provided so far, the literature do not address the effects of uncertainties related to fiscal imbalances. Thus, unlike the studies addressing the effect of disagreement in expectations on the risk premium, our study seeks evidence for the influence of the disagreement in expectations about public debt on the risk premium. This relation is possible to be done once economic theory and empirical evidence indicate a causal connection between fiscal discipline and inflation: the presence of high fiscal imbalance can start an inflationary process (Mishkin and Savastano, 2001). The literature emphasizes that fiscal discipline is essential to a low and stable inflation rate (Fatás and Mihov, 2003; Wyplosz, 2005, de Mendonça and Silva, 2016). Catão and Terrones (2005) find that fiscal deficits are inflationary in most countries, and this relationship is especially strong for developing economies and for countries with high inflation rates. They also find that fiscal deficits have a significant bearing on long-run inflation among countries within a “moderate” inflation range. In contrast, fiscal deficits appear to have no significant positive effect on long-run inflation among developed countries with a long history of low single-digit inflation. Regarding the US economy , Sims (2011) argue that fiscal policy underwent dramatic shifts in the 1970s and economic theory makes clear that in an environment of uncertainty about future fiscal policy, monetary policy instruments may lose potency or have perverse effects. He presents a theoretical framework which aims at understanding the effects of fiscal uncertainties on monetary policy. He shows that fiscal variables have predictive value in dynamic models, even if traditional monetary policy indicators are included in the

system. Sims (2011) argues that fiscal policy can be a primary transmission mechanism or a primary source for changes in the inflation rate. Despite the theoretical view that fiscal deficits are inflationary, empirical studies have yet to provide a significant connection between fiscal deficits and inflation across a broad range of countries and inflation rates. In this sense, Lin and Chu (2013) seek to investigate whether fiscal deficits are inflationary. They examine the deficit-inflation relationship in 91 countries from 1960 to 2006. Their findings show that the fiscal deficit has a strong impact on inflation in high-inflation episodes, and has a weak impact in low inflation episodes. The model developed by Bianchi and Melosi (2013) accounts for persistent and accelerating increases in inflation and for the heterogeneity, across countries and over time, of the link between inflation and fiscal discipline. According to them, when agents are uncertain about the way debt will be stabilized, the strict distinction between Ricardian and non-Ricardian regimes typical of the literature on the fiscal theory of price level breaks down. In its stead, a continuum of regimes reflecting agents’ beliefs about the future conduct of fiscal and monetary policies arises. As agents observe more and more deviations from a virtuous regime in which the central bank has full control of inflation, they become increasingly convinced that debt will be inflated away. This implies that the law of motion characterizing the economy evolves over time in response to what agents observe. Bianchi and Melosi (2013) introduced the notion of dormant shocks – which are shocks that move the debt-to-GDP ratio and that have no effect on the macroeconomic variables when policymakers behave according to a virtuous regime. However, as policymakers start deviating from such a regime and agents become more and more discouraged about the possibility of moving back to the virtuous regime, the effects of the dormant shocks arise, with a progressive increase in inflation and uncertainty. Therefore, the model is able to generate a persistent and accelerating run-up in inflation as relatively optimistic agents become more and more pessimistic. Regarding the process of expectation formation and the role expectation plays in the economy, the literature on disagreement in expectations (especially in the fields of macroeconomics and finance) has emphasized the fact that agents disagree about the future behavior of the economy to the extent that uncertainties emerge in the economy (e.g., Mankiw et al., 2003).4 Analyzing survey data on expectations, either of the general public or of professional forecasters, it is observed that disagreement in expectations is substantial and varies over time due to changes in uncertainties (Montes et al. 2016). The degree of disagreement in expectations about the future state of a certain variable (such as, inflation, GDP, exchange rate or public debt) reflects the degree of uncertainty faced by people (such as investors) who are trying to forecast the future behavior of this variable, as well differences in prior beliefs or models used by them. There exist several articles discussing the effects of the disagreement in expectation on the economy (e.g., Mankiw et al., 2003; Scheinkman and Xiong, 2003; Hong and Stein, 2007; Lorenzoni, 2009; Söderlind, 2009 and 2011; Wright, 2011; Buraschi and Whelan, 2012; Carlin et al., 2014; Angeletos and La’O, 2013; Burnside et al., 2016; Ehling et al., 2016). In relation to the effect of disagreement in expectations on the yield curve, Ehling et al. (2016) show that there exists a statistically and economically positive relation between 4

The literature on disagreement has discussed issues like its sources, its consequences, how to measure the phenomenon and how to link disagreement with macroeconomic uncertainty (e.g., Patton and Timmermann, 2010; Dovern et al., 2012; Andrade et al., 2014; Montes et al. 2016).

inflation disagreement and nominal yields across all maturities after controlling for expected inflation. Moreover, they show that inflation disagreement raises real and nominal yields and their volatilities. BEIRs reflect the overall inflation compensation requested to hold nominal bonds, comprising both the expected level of inflation and a premium to compensate for inflation risks. From a policy perspective, understanding the dynamics of the inflation risk premium is crucial. In this sense, the next sections aim at providing new evidence on the determinants of the inflation risk premium in Brazil. 3. Data and Methodology Below, we explain the three main variables of the study (the inflation risk premium, the disagreement in expectations about public debt and the credibility index). To obtain the inflation risk premium (RPm), we use the methodology proposed by Ciccarelli and Garcia (2009), Söderlind (2011) and Wright (2011) based on a modern Fisher equation. Thus, we use the difference between the nominal interest rate (im) and the real interest rate (rm) to compute the break-even inflation rate (BEIR), and compare with the expected inflation rate (Expect_inflm).5 We apply this calculus to four maturities (m), where, m is 12, 24, 36 and 48 months ahead. It is important to note that we transform the usual yield curve of nominal and real interest rate in spot rates by srtm = ((pt(m-12) / ptm) – 1). Where sr is the rate (nominal or real), t the day of the rate, m is the maturity (12, 24, 36 and 48 months) and p is the price of the bond (nominal or real). The nominal (im) and real (rm) interest rates are daily, obtained between 01/28/2005 and 12/30/2015 and extracted from BMF&BOVESPA. Figure 1 presents both nominal and real spot rates (monthly average) for 12, 24, 36 and 48 months ahead. < Figure 1 here > The expected inflation rates (Expect_inflm) with the same four maturities are provided by the Central Bank of Brazil (CBB) through the so-called “Focus-Market Readout”6. Based on Söderlind (2011) and Kajuth and Watzka (2011), the inflation risk premium (RPm) equation (the “break-even deviation”) can be described based on a modern Fisher Equation: 𝑅𝑃𝑡𝑚 = 𝑖𝑡𝑚 − 𝑟𝑡𝑚 − 𝐸𝑥𝑝𝑒𝑐𝑡_𝑖𝑛𝑓𝑙𝑡𝑚

(1)

According to Söderlind (2011), the observed “break-even deviation” (i − r − πe) depends positively on the inflation risk premium and negatively on the liquidity premium on real bonds. However, for the Brazilian interest rate, the liquidity premium is not priced because the inflation linked bonds are held to maturity by pension funds. Thus, following Söderlind (2011) and based on a modern Fisher equation, our dependent variable in the regressions is the “break-even deviation” – which is a proxy for the inflation risk premium. 6 Focus-Market Readout presents the results of Gerin’s market expectations survey, a daily survey of forecasts of roughly 120 banks, asset managers and other institutions (real sector companies, brokers, consultancies and others) for the Brazilian economy. The survey of market expectations began in May 1999 as part of the transition to the inflation targeting system. The survey was created in order to monitor market expectations regarding the main macroeconomic variables, and improve the inputs for the monetary policy decisionmaking process. The system calculates sample statistics from the data gathered in real time, and thereby enables the generation of daily reports for the members of the Board. One of these reports, the Focus-Market Readout, is published every Monday at the Central Bank website at the internet. 5

Table 1 presents the descriptive statistics for the term structure of the risk premium (RP). Figure 2 presents the break-even inflation rate (BEIRtm = itm – rtm), the inflation expectation (Expect_inflm) and the risk premium (RPm). We observe that the average term structure of the risk premium is positive, which is in accordance to Ciccarelli and Garcia (2009). The negative risk premium in the short maturity is also observed by them. It happens when the inflation expectation increases faster than the nominal bond. < Table 1 here > < Figure 2 here > Since the 1990s the concern with inflation has brought several countries to adopt IT. After more than a decade, studies indicate that the adoption of IT represents a success in the control of inflation (e.g., Lin and Ye, 2009; de Mendonça and de Guimarães e Souza, 2012). However, one of the preconditions to the success of IT is the fiscal balance and the commitment to public debt sustainability. A sound fiscal position is essential to any economy and particularly to IT developing countries. And this is because in the case where the government is not committed to fiscal balance, the result is a pressure on inflation due to the risk of using an expansionary monetary policy to finance the public debt (de Mendonça and Silva, 2016). Therefore, due to the existing relationship between government fiscal commitment and inflation, to the history of fiscal imbalances in the Brazilian economy, and to existing concerns related to public debt sustainability, we are interested in the effects of both expectations formed for the public debt and disagreement in these expectations over the risk premium. Based on Montes et al. (2016) and Oliveira and Curi (2016), the series for the disagreement in expectations about public debt is built upon a survey of expectations provided by the CBB.7 In order to better understand its construction, it is worth presenting the following notation: t is the instant of time the projection is made8, i identifies the agent who releases the forecast ( i  , where I is the set of agents surveyed9), ND is the forecast about net public debt to GDP, so, Ei,tNDa+j represents the projection that the i-th agent release at time t about the value of the net public debt to GDP will take in the end of year a+j10. In turn, Etmin(ND) a+j=min(Ei,t(ND)a+j, i ∈ I) and denotes the minimum value of the distribution, while, Etmax(ND)a+j=max(Ei,t(ND)a+j, i∈I) denotes its maximum value.

7

The CBB release the maximum, minimum, median, mean, coefficient of variation and standard deviation statistics of the distribution of the daily forecast for the net public debt (ND) in fixed event for the end of the current year and four years ahead. 8 This instant is characterized by a specific date, namely, a day d, a month m and a year a. 9 The number of agents in  is I. 10 j=0: current year; j=1: next year immediately after the current year; j=2: two years after the current year; j=3: three years after the current year; j=4: four years after the current year.

The measure of disagreement that we use throughout this paper is Disag_NDta+j.11 computed by the range of the distribution defined as: Disag_NDta+j = Etmax(ND)a+j

Etmin(ND)a+j

(2)

Forecasts such as Ei,tNDa+j are known as fixed event ones because the forecasting horizon varies with the passage of time. Indeed, the prospective period of forecasts made at t for the value that the variable ND will take in the end of the year a + j decrease as t progress within a, the year in which expectations are made.12 This pattern of decreasing forecasting horizons as t advances through the year brings about a seasonal behavior in disagreement measures based on fixed event forecasts because expectations dispersion tends to decrease as the forecasting horizon shrinks13. It is to avoid this seasonal behavior inherent to disagreement measures based on fixed event forecasts that most articles in the literature (e.g., Mankiw et al. (2003); Patton and Timmermann (2010); Dovern et al. (2012)) recur to fixed horizon forecasts, in which the forecasting horizon does not vary with the passage of time. As proposed in Dovern et al. (2012), the conversion of fixed event forecasts into fixed horizon ones is accomplished by applying the formula below: Et X

12 j 1



12   m  1 m 1 Et X a  j  Et X a  j 1 , j  0,1, 2,3, 12 12

(3)

Where m represents the month in which the projection is made (or the month containing period t) and EtX12(j+1) denotes the average of agents’ expectations about the value that the variable X (which is ND) will take at the end of the next 12(j+1) months. The same formula is used to interpolate minimum and maximum projections in order to calculate the disagreement in expectation (as well the average expectations). In the end of the process, we derive a term structure of disagreement in expectations, which is comprised by the 11

Like Oliveira and Curi (2016), we use this measure of disagreement throughout the paper, as other measures require the knowledge of the entire distribution of expectations. Such information is not provided by the CBB. We are aware of the fact that papers on disagreement often use other measures, such as the interquartile range and Kulback-Liebler divergence measure. These two options, though, cannot be calculated without the entire distribution of individual forecasts. The standard deviation – SD(ND) – and the coefficient of variation – CV(ND) – are also frequently used as measures of disagreement. Nevertheless, although these alternative measures are released, the interpolation of the SD(ND) and CV(ND) to transform in fixed horizon is not appropriate for the analysis (see, for instance, Oliveira and Curi (2016)). Thus, it is not possible to reestimate the equations with such measures. Still, like Oliveira and Curi (2016) have done, we show in Appendix A that our measure of disagreement (Disag_ND) and both SD(ND) and CV(ND) provide similar results. 12 An example could help to clarify this issue. Suppose that an agent, in March 2000, computes his expectation about the value of the inflation rate in the end of 2000. In this case we can say that the time horizon of the forecast is 10 months because the first 2 months of 2000 have already passed and inflation figures for January and February are known. By the same line of reasoning, when this agent computes his inflation expectation in September 2000 about the value of the inflation rate at the closing of 2000, the time horizon of his forecast decreases to only 4 months. 13 Indeed, the disagreement measure observed in March 2000 for the value that the inflation rate will take in the end of 2000 tends to be greater than the disagreement measure observed in September 2000 for the value that the same variable will take at the closing of 2000. The divergence measure tends to increase again in March 2001, since the current year becomes 2001 and the time horizon of the forecast becomes 9 months.

“vertices” DisagtND12, DisagtND24, DisagtND36, DisagtND48. As the CBB discloses forecasts for the current and the next four years, the formula above can be applied by taking j = 0,1,2,3,4. Therefore, we can always interpolate forecasts for the fixed time horizons of 12, 24, 36 and 48 months. Figure 3 shows the disagreement in expectations about net public debt to GDP (Disag_NDtm) (for 12, 24, 36, 48 Months ahead). The procedure described above is performed daily, allowing us to study the term structures of disagreement for each business day. Time series comprised of daily observations are converted to the monthly frequency by monthly averages. The conversion of fixed event forecasts into fixed horizon and the monthly frequency were applied to compute the disagreement in expectations about net public debt to GDP (Disag_NDtm), the average expectation of inflation (Expect_inflm) used to compute the risk premium, the expectations of GDP Growth (Expect_GDP48) and the expectation about net public debt to GDP (Expect_NDm). < Figure 3 here > After computing the four maturities of the inflation risk premium (RPm), the disagreement in expectations about net public debt to GDP (Disag_NDtm) and the average expected net public debt to GDP (Expect_NDm), the final step is to extract the first principal component of these series with four maturities (12, 24, 36, 48 months); these components are good proxies for their common trend. The application of this technique has a long tradition in the study of conventional yield curves (Litterman and Scheinkmann, 1991), which justifies its application to the term structures that we study here. As the monthly averages, it also allows filtering out erratic shifts on a given disagreement measure that do not reflect upon the others. Such movements can be regarded as outliers, thus, they should be ignored from the economic point of view. In turn, the monetary policy credibility index (Credibt) is based on the idea of Agénor and Taylor (1992) that series of expected inflation could be applied to derive a credibility index. As Svensson (2000) proposed, the credibility can be measured by the difference between expected inflation and the target. In this sense, the credibility index is the index proposed by de Mendonça (2007).14 The index uses the series of inflation expectations obtained from the CBB, the inflation target defined by the monetary authority and the tolerance bands. The credibility index has a value equal to 1 when the annual expected inflation ((Expect_infl12) is equal to the target (InflT) and decreases in a linear way while inflationary expectation deviates from the announced target. Therefore, the credibility index shows a value between 0 and 1 strictly if the expected inflation is situated between Although different indexes of credibility have been proposed – as summarized in the works of de Mendonça and de Guimarães e Souza (2009) and Nahon and Meurer (2009) – and therefore there is a variety of indexes of credibility capable of being used in empirical analyses, the present work does not seek to analyze the influence and power of each index on monetary policy in Brazil – although such research is important. Thus, the option for using the index proposed by de Mendonça (2007) is due to the following arguments: i) the index is recognized by international literature, being this index used in several applied studies; ii) simplicity of understanding and preparation; iii) the index captures the changes and fluctuations in credibility in a way compatible with the regime of inflation targeting adopted in Brazil, i.e., the index uses predetermined tolerance bands, and not ad-hoc tolerance bands as proposed by other indices; and iv) the index is rigorous enough and punishes appropriately deviations of inflation expectations in relation to the inflation target. 14

the maximum and minimum limits (Infl*) established for each year and assumes a value equal to 0 when the expected inflation exceeds one of these limits. The idea of the index is to capture the degree of anchorage in a normalized index (between 0 and 1). In this sense when the inflation expectation is above the inflation target (and at the same time it did not exceed the upper limit of the band), we use, in the denominator, the difference between the maximum limit (Infl*MAX) and the inflation target (InflT). But, when the inflation expectation is below the inflation target (and at the same time it did not exceed the lower limit of the band), we use, in the denominator, the difference between the minimum limit (Infl*MIN) and the inflation target (InflT). Hence: 𝑖𝑓 𝐸𝑥𝑝𝑒𝑐𝑡_𝑖𝑛𝑓𝑙12 = 𝐼𝑛𝑓𝑙𝑡𝑇 1 ∗ ∗ 𝐸𝑥𝑝𝑒𝑐𝑡_𝑖𝑛𝑓𝑙12 − 𝐼𝑛𝑓𝑙𝑡𝑇 , 𝑖𝑓 𝐼𝑛𝑓𝑙𝑡𝑀𝐼𝑁 < 𝐸𝑥𝑝𝑒𝑐𝑡_𝑖𝑛𝑓𝑙12 < 𝐼𝑛𝑓𝑙𝑡𝑀𝐴𝑋 𝐶𝑟𝑒𝑑𝑖𝑏 = 1 − 𝐼𝑛𝑓𝑙𝑡∗ − 𝑖𝑛𝑓𝑙𝑡𝑇 ∗ ∗ 0, 𝑖𝑓 𝐸𝑥𝑝𝑒𝑐𝑡_𝑖𝑛𝑓𝑙12 ≥ 𝐼𝑛𝑓𝑙𝑡𝑀𝐴𝑋 𝑜𝑟 𝐸𝑥𝑝𝑒𝑐𝑡_𝑖𝑛𝑓𝑙12 ≤ 𝐼𝑛𝑓𝑙𝑡𝑀𝐼𝑁 1,

(4)

We also check for the effects of macroeconomic variables. Thus, we analyze the effect of the observed inflation rate (Infl) (this series uses the inflation rate accumulated in 12 months; IPCA – series code 13522 obtained from the CBB database), the first principal component of the term structure of expectation of Net Debt as a percentage of GDP (Expect_ND), the expected GDP growth four years ahead (Expect_GDP48) computed by the conversion of fixed event forecasts into fixed horizon technique explained above, and the country risk (Embi) measured by JP Morgan and obtained from IPEA Data (series EMBI+ Risco-Brasil; daily series converted in monthly by the averages)15. Regarding the expected effects on the risk premium, we expect that RP is positively affected by ∆Expect_GDP48, ∆Infl e ∆Expect_ND. In turn, since the disagreement in expectations about net public debt to GDP (Disag_ND) captures the uncertainty about the fiscal side (in particular, regarding debt management), we expect that an increase in this variable causes an increase in the risk premium. The Embi is a risk premium priced by foreign investors and acts as a control for possible non-inflationary disturbances. It is expected a positive relation between the country risk (Embi) and the risk premium. Credibility is expected to reduce the inflation risk premium because a credible monetary policy reduces uncertainty about future inflation.16 The econometric analysis makes use of Ordinary Least Squares (OLS)17 and Generalized Method of Moments (GMM). Due to the risk of endogeneity problems, GMM is chosen to deal with these problems (Hansen (1982)). As pointed out by Wooldridge (2001), the use of the GMM estimator with its overidentifying restrictions is a more 15

The idea of adding the country risk (Embi) follows Vieira and Holland (2003) which found evidence for the “default fear” hypothesis in Brazil. Vieira and Holland (2003) found a positive relationship between country risk (Embi) and interest rate. 16 In relation to the effects of the main variables (Disag_ND, Credib and Expect_ND) on the difference between im and rm, it is expected that an increase in the disagreement in expectations about net public debt to GDP and an increase in the expectations formed for this variables cause an increase in the break-even inflation rate (BEIR), which is an indicator of inflation expectations obtained from the difference between nominal and real interest rates. Moreover, it is expected that when the monetary policy is credible, the central bank needs less effort to control inflation, and as a consequence, changes in the nominal interest rate are lower, reducing the break-even inflation rate (BEIR). 17 Due to the problems of autocorrelation and heteroskedasticity (Table B.1 presents the results of the tests – Appendix B), the reported t-statistics in the OLS estimates are based on the estimator of Newey and West (1987).

efficient estimator than OLS. Besides, according to Baum et al. (2007), the use of GMMHAC (heteroscedasticity and autocorrelation consistent – see Davidson and MacKinnon, 2004) is more appropriate than, for example, IV method. Although GMM estimator is a more efficient estimator than OLS, the estimates through OLS are kept in the paper since they indicate the expected signs of the coefficients. For a more efficient GMM estimator than OLS, overidentifying restrictions need to be considered (Wooldridge, 2001). Therefore, with the intention of testing the validity of the overidentifying restrictions, a standard J-test is performed (Hansen (1982)). GMM estimates adopted a standard procedure based on Johnston (1984), i.e., the chosen instruments were dated to the period t-1 or earlier. Cragg (1983) pointed out that overidentification analysis has an important role in the selection of instrumental variables to improve the efficiency of the estimators. 4 – Empirical Analysis Figure 4 presents the scatter plot with the regression line and the correlation between the inflation risk premium (RP) and the main variables that we use in the analysis. The disagreement has a positive correlation with the risk premium, and it presents the greatest correlation (0.59). In addition, we observe positive correlations between Infl and RP and Expect_ND and RP; and negative correlation between Credib and RP. It is important to note that we analyze the general level of the series (or the first principal component) – like Montes et al. (2016) and Oliveira and Curi (2016) have done – rather than the four maturities. < Figure 4 here > The use of time series data in equations estimations demands to verify whether the series in the model have a unit root (non-stationary data series) to avoid the possibility of spurious regression. Hence, we perform the unit root tests – Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) – (Table 2). According to the criterion that when at least two of the three tests indicate that the series does not have a unit root, the series is considered stationary, one can see that only the inflation risk premium (RP) is I(0), and all other variables are I(1). We use ∆ as the firstdifference operator. < Table 2 here > Aiming at analyzing the influence of macroeconomic variables to explain the risk premium, we estimate the following baseline econometric model (equation 5). In order to avoid spurious regression, all the variables that are I(1) enter in the equation after firstdifference transformation. 𝑅𝑃𝑡 = 𝛽0 + 𝛽1 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝐺𝐷𝑃𝑡 48 + 𝛽2 ∆𝐼𝑛𝑓𝑙𝑡 + 𝛽3 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝑁𝐷𝑡 + ℰ1,𝑡

Where, ε1,t is a random error term.

(5)

Aiming at analyzing the effects of disagreement in expectations about net public debt to GDP and monetary policy credibility on the inflation risk premium, we estimate different variants of the baseline econometric model (equations 6, 7 and 8). From equation 6 we also test the effect of the country risk (Embi). 𝑅𝑃𝑡 = 𝛽4 + 𝛽5 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝐺𝐷𝑃𝑡 48 + 𝛽6 ∆𝐼𝑛𝑓𝑙𝑡 + 𝛽7 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝑁𝐷𝑡 + 𝛽8 ∆𝐸𝑚𝑏𝑖𝑡 + ℰ2,𝑡

(6)

𝑅𝑃𝑡 = 𝛽9 + 𝛽10 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝐺𝐷𝑃𝑡 48 + 𝛽11 ∆𝐼𝑛𝑓𝑙𝑡 + 𝛽12 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝑁𝐷𝑡 + 𝛽13 ∆𝐸𝑚𝑏𝑖𝑡 + 𝛽14 ∆𝐷𝑖𝑠𝑎𝑔_𝑁𝐷𝑡 + ℰ3,𝑡 𝑅𝑃𝑡 = 𝛽15 + 𝛽16 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝐺𝐷𝑃𝑡 48 + 𝛽17 ∆𝐼𝑛𝑓𝑙𝑡 + 𝛽18 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝑁𝐷𝑡 + 𝛽19 ∆𝐸𝑚𝑏𝑖𝑡 + 𝛽20 ∆𝐷𝑖𝑠𝑎𝑔_𝑁𝐷𝑡 + 𝛽21 ∆𝐶𝑟𝑒𝑑𝑖𝑏𝑡 + ℰ4,𝑡

(7)

(8)

where, ε2,t , ε3,t and ε4,t are random error terms. Table 3 shows the estimates and provides: (i) the results obtained from the baseline model; (ii) the results obtained by considering the effect of the disagreement, and; (iii) the results obtained by considering the effect of the credibility. < Table 3 here > Regarding the estimates in Table 3, the coefficients for the influence of both ΔExpect_GDP48 and Δinfl have the expected signs in all specifications and present statistical significance in all GMM estimates. These findings are compatible with Ciccarelli and Garcia (2009), which argue that an increase in the economic activity growth rate is perceived by market participants as fuel to inflation pressures.18 It is noteworthy that, in all specifications, ΔExpect_ND is significantly positive, and this is consistent with the general hypothesis that excessive debt leads to higher money issuance and also to a higher inflation component of the nominal interest rate. In turn, a novelty of our study concerns the effect of the disagreement in expectations about net public debt to GDP. The estimated coefficients for ΔDisag_ND have positive signs in all specifications and statistical significance in all GMM estimates. These findings reveal the expectations for the fiscal side play an important role for the behavior of the inflation risk premium. Another novelty is the effect of monetary policy credibility on the inflation risk premium. The estimates present negative and significant coefficient in the GMM estimate. Thus, when credibility is enhanced, the inflation risk premium tends to reduce. It is important to note that though the dependent variable (the risk premium) contains the expected inflation, the credibility index is capturing the dispersion of the expected inflation in relation to the inflation target. In this sense, the credibility index captures the degree of 18

Once economic agents expect an acceleration of economic growth, there is the possibility of pressure on inflation. If the Central Bank shows little success in making inflation converge to the target (as is the case of the Central Bank of Brazil in recent years), agents may require a higher risk premium. In Brazil, the real interest rate is negotiable as much as the nominal interest rate. Therefore, when investors expect a higher inflation scenario due to the acceleration of economic growth and due to loose monetary policy by the central bank, they demand more inflation-linked bonds (with real interest rates) and reduce their exposure to nominal interest rates. For this reason, nominal bonds tend to depreciate relative to inflation-linked bonds, thus increasing the BEIR. This effect is evidenced by the positive sign of the expected economic activity growth used in the equation.

anchorage of inflation expectations (formed by financial markets experts) in relation to the inflation target. Thus, to the extent that the process of anchorage is compromised (due, for instance, to inflation deterioration) the inflation risk premium is affected, reflecting the lack of commitment of the central bank with the Inflation Targeting regime. These results suggest the following insights: (i) a stronger anchorage of inflation expectations represents an important attribute to reduce the inflation risk premium, and (ii) the lower the disagreement in expectations about net public debt to GDP, the lower is the inflation risk premium. Therefore, to the extent that these aspects affect the inflation risk premium, they also affect the conduction of monetary policy. 5. Robustness analysis We extend the analysis in order to provide robust results. Thus, we estimate the model using the autoregressive distributed-lag (ARDL) cointegration method proposed by Pesaran and Shin (1999) and Pesaran, et al. (2001). This method is useful because it allows one to transform the model into a long-run representation showing the response of the dependent variable to changes in the explanatory variables. Moreover, the method has advantages in comparison to standard cointegration tests because it is consistent with small samples and it can be applied to a mix of variables I(0) and I(1) in the cointegrating relationship. In order to perform the ARDL cointegration proposed by Pesaran et al., (2001), the error correction model in this analysis corresponds to: 𝑝

∆𝑅𝑃𝑡 = 𝛼0 +

𝑝

𝑖=1

𝑝

𝛾𝑖 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝐺𝐷𝑃𝑡−𝑖 48 +

𝜑𝑖 ∆𝑅𝑃𝑡−𝑖 + 𝑖=0 𝑝

+

𝑖=0

𝑝

𝜏𝑖 ∆𝐸𝑥𝑝𝑒𝑐𝑡_𝑁𝐷𝑡−𝑖 + 𝑖=0

𝜔𝑖 ∆𝐸𝑚𝑏𝑖𝑡−𝑖 𝑖=0

𝑝

𝜗𝑖 ∆𝐶𝑟𝑒𝑑𝑖𝑏𝑡−𝑖 + 𝛿1 𝐸𝑥𝑝𝑒𝑐𝑡_𝐺𝐷𝑃𝑡−1 48 + 𝛿2 𝐼𝑛𝑓𝑙𝑡−1 + 𝛿3 𝐸𝑥𝑝𝑒𝑐𝑡_𝑁𝐷𝑡−1

𝜌𝑖 ∆𝐷𝑖𝑠𝑎𝑔_𝑁𝐷𝑡−𝑖 + 𝑖=0

𝑝

𝜃𝑖 ∆𝐼𝑛𝑓𝑙𝑡−𝑖 +

𝑖=0

+ 𝛿4 𝐸𝑚𝑏𝑖𝑡−1 + 𝛿5 𝐷𝑖𝑠𝑎𝑔_𝑁𝐷𝑡−1 + 𝛿6 𝐶𝑟𝑒𝑑𝑖𝑏𝑡−1 + 𝜉𝑡0

(9)

Where, p is the optimal lag length. The second part of the right-hand side with parameter (i= 1, 2, 3, 4, 5, 6) represents the long run relationship. An F-test is carried out to check the existence of long run relationship. When a long run relationship exists, the F-test indicates which variable should be normalized. The null hypothesis for the non-existence of the long-run relationship among variables in equation (9) is H0: δ1 = δ2 = δ3 = δ4 = δ5 = δ6 = 0 against the alternative hypothesis H1: δ1 ≠ δ2 ≠ δ3 ≠ δ4 ≠ δ5 ≠ δ6 ≠ 0. Pesaran et al., (2001) provide critical values for the cases where all regressors are I(0) for the lower bound and the cases where all regressors are I(1) for the upper bound. If the reported F-test statistic exceeds their respective upper critical values, then the null hypothesis of no cointegration can be rejected. If the F-test statistic lies between the lower and upper bounds there is a need to determine the order of integration of the variables before proceeding to the analysis. When cointegration is confirmed, the next step is to determine the lag orders for the variables in the model. Thus, the model which optimizes the Adjusted R-squared is

selected. Finally, before computing the long-run coefficients, we verify if the errors of the models are serially independent.19 The estimation is presented below (table 4). The findings presented in table 4 suggest that the long-run coefficients for the ARDL estimation do not present significant changes in terms of expected signs based on economic theory and statistical significance (except the Embi, which does not present statistical significance). The results point to the following policy implications. First, in order to reduce the inflation risk premium, the government should adopt policies based on fiscal discipline, which are able to provide fiscal balance, and thus to reduce both the expected public debt to GDP and the disagreement in expectation about public debt in relation to GDP. Second, the central bank’s commitment to keep inflation low and stable and the credibility of the monetary policy under inflation targeting are important aspects to reduce the inflation risk premium. < Table 4 here > 6. Conclusion Studies seek to understand how the break-even inflation rates differ from survey data on inflation expectations. Based on a modern Fisher equation, these studies address the determinants of the observed “break-even deviation”. Different from the existing studies, this paper analyzes the determinants of the inflation risk premium in Brazil during the inflation targeting period between 2005 and 2015. In particular, the paper provides evidence for the influence of the disagreement in expectations about the public debt as well as of the monetary policy credibility on the inflation risk premium. So far, there are no studies addressing these relations. Thus, the paper contributes to the literature since it is the first to analyze these effects and it is the first to analyze these effects for an inflation targeting developing economy. The paper finds empirical evidence that an increase in the disagreement in expectation about public debt in relation to GDP and a reduction in the credibility are able to increase the inflation risk premium in Brazil. The study brings two important policy implications. One related to the effect of the expectations formed for the commitment of the government with debt management; and the other related to the effect of the expectations formed for the central bank’s commitment with the Inflation Targeting regime. The results suggest the reduction of the disagreement in expectations about the public debt brings beneficial consequences for the inflation risk premium. Furthermore, the findings also suggest that the commitment to keep a low and stable inflation rate and the degree of anchorage of inflation expectations in relation to the inflation target (i.e., the monetary policy credibility) determine the inflation risk premium.

19

Figure B.1 (Appendix B) presents the correlogram of residuals.

Appendix A - Correlation between two alternative measures of disagreement in expectations

The Central Bank of Brazil (CBB) releases the maximum, minimum, median, mean, coefficient of variation (CV(ND)) and standard deviation (SD(ND)) statistics of the distribution of the daily forecast for the net public debt in fixed event for the end of the current year and four years ahead (as described in section 3 “Data and Methodology”). This appendix compares the measure of disagreement in expectations (Disag_NDt) used throughout this work, which is the range of the distribution of individual expectations, with two alternative measures of disagreement, the standard deviation - SD(ND) - and the coefficient of variation - CV(ND). Although these alternative measures are released, the interpolation of the SD(ND) and CV(ND) to transform in fixed horizon is not appropriate for the analysis (see, for instance, Oliveira and Curi (2016)). Thus, it is not possible and it would make no sense at all re-estimate the equations with such measures. Table A.1 below shows the correlation between the original daily SD(ND) and CV(ND) released by the CBB with the measure of disagreement (Disag_ND) which we calculated based on maximum and minimum expectations for the end of each year between 2005 and 2015. Each row present specific alternative measures of disagreement - SD(ND) or CV(ND) - and each column refers to a given year. Cells inform the correlation between the measures of disagreement in expectations, which are formed for the closure of the year informed in the heading of the table. For example, the column referring to 2006 shows that the correlations between the series formed by the standard deviations (SD(ND)) and the ranges of the distributions of expectations (Disag_ND) for the closing of 2006 is 0.977 and in the case of the coefficient of variation (CV(ND)) is 0.975. The correlation coefficients are greater than 0.9 in most of the cases, which allows to conclude that both measures provide similar results. < Table A.1 here > Table A.2 shows the results for the same analysis with monthly series calculated as the average of the daily forecast observed in a given month. The same was done for the standard deviation and the coefficient of variation. For example, the column referring to 2014 shows that the correlations between the series formed by the SD(ND) and Disag_ND for the closing of 2014 is 0.936 and in the case of the CV(ND) is 0.959. The correlation coefficients are greater than 0.9 in most of the cases, which allows to conclude that both measures provide similar results. < Table A.2 here >

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Figure 1 – Nominal (i) and real (r) spot interest rates (12, 24, 36, 48 maturities – 2005M01 to 2015M12)

Figure 2 – Break-even inflation rate (BEIR), inflation expectation (Expect_infl) and risk premium (RP) (12, 24, 36, 48 Months ahead – 2005M01 to 2015M12)

Figure 3 – Disagreement in expectations about net public debt to GDP (Disag_ND) (for 12, 24, 36, 48 Months ahead – 2005M01 to 2015M12 (%))

6

6

5

5

4

4

3

3

2

2

RP

RP

Figure 4 – Scatter plot and correlation – 2005M01 to 2015M12 – risk premium (RP), observed inflation rate (Infl), expectation of Net Debt as a percentage of GDP (Expect_ND), credibility (Credib) and Disagreement in expectations about net public debt to GDP (Disag_ND)

1

0

-1

-1

-2

-2 -3

-3 3

4

5

6

7

8

9

Infl

10

-3

11

-2

-1

0

Expect_ND

0.55

6

6

5

5

4

4

3

3

2

2

RP

RP

1

0

1

2 0.23

1

0

0

-1

-1

-2

-2

-3

1

-3 -4

-2

0

2

4

Disag_ND

6

8 0.59

10

0.0

0.2

0.4

0.6

Credib

0.8 -0.11

1.0

Date: 08/30/16 Tim e: 15:02 Sam ple: 2005M01 2015M12 Included obs ervations : 124 Q-s tatis tic probabilities adjus ted for 8 dynam ic regres s ors

Figure B.1 – Correlogram of residuals (ARDL) Autocorrelation

Partial Correlation

AC 1 2 3 4 5 6 7 8 9 1... 1... 1... 1... 1... 1... 1... 1... 1... 1... 2... 2... 2... 2... 2... 2... 2... 2... 2... 2... 3... 3... 3... 3... 3... 3... 3...

0.106 -0.06... -0.00... 0.000 -0.05... -0.04... -0.10... -0.08... -0.05... -0.09... -0.11... -0.14... 0.008 -0.04... 0.016 -0.08... -0.03... 0.076 0.039 0.054 0.101 -0.00... 0.212 0.163 -0.08... -0.09... -0.06... -0.03... -0.07... -0.12... -0.07... 0.064 0.062 -0.05... -0.01... 0.114

PAC 0.106 -0.07... 0.012 -0.00... -0.05... -0.03... -0.10... -0.06... -0.05... -0.10... -0.11... -0.16... -0.01... -0.11... -0.02... -0.17... -0.10... -0.02... -0.09... -0.02... -0.00... -0.11... 0.168 0.062 -0.09... -0.09... -0.10... -0.05... -0.08... -0.14... -0.09... 0.020 0.016 -0.09... 0.003 0.047

*Probabilities m ay not be valid for this equation s pecification.

Q-Stat 1.4406 1.9816 1.9838 1.9838 2.4182 2.6579 4.0955 4.9735 5.3689 6.5308 8.3937 11.465 11.473 11.776 11.813 12.958 13.097 13.948 14.169 14.601 16.138 16.139 23.110 27.283 28.441 29.783 30.470 30.622 31.509 33.995 34.810 35.510 36.165 36.688 36.742 39.050

Prob... 0.230 0.371 0.576 0.739 0.789 0.850 0.769 0.760 0.801 0.769 0.678 0.490 0.571 0.624 0.693 0.676 0.730 0.732 0.774 0.799 0.762 0.809 0.454 0.291 0.288 0.277 0.293 0.334 0.342 0.281 0.291 0.306 0.323 0.345 0.388 0.334

Table 1 – Descriptive statistics – Risk Premium (2005M01 to 2015M12) Median

Std. Dev

Kurtosis

Skewness

Minimum

Maximum

Observations

RP_12

Mean 0.003%

0.047%

0.0056

2.730

-0.835

-2.448%

1.269%

132

RP_24

0.634%

0.538%

0.0079

6.054

1.935

-0.551%

3.949%

132

RP_36

0.820%

0.752%

0.0066

2.321

1.313

-0.294%

3.394%

132

RP_48

0.958%

0.846%

0.0070

0.194

0.778

-0.445%

3.013%

132

Statistics

Table 2 – Unit root and stationarity tests (ADF, PP and KPSS) ADF Test

Series

PP Test La g

Test

RP

1

c

Expect_GDP48

1

b

48

0

b

Infl

1

c

Δinfl

0

c

Expect_ND

1

c

ΔExpect_ND

0

c

Embi

1

c

ΔEmbi

0

c

Credib

2

b

ΔCredib

1

c

ΔExpect_GDP

Disag_ND

0

b

ΔDisag_ND

0

c

2.43 6 0.00 2 8.95 5 0.30 9 6.55 6 1.22 4 6.47 8 0.31 3 8.62 7 3.35 1 9.36 7 2.16 0 8.30 7

5% Critica l Value

La g

Test

-1.943

2

c

-3.444

0

b

-3.444

4

b

-1.943

5

b

-1.943

1

c

-1.943

6

b

-1.943

4

c

-1.943

4

c

-1.943

2

c

-3.444

1

b

2.04 3 0.46 5 8.95 1 1.45 0 6.66 4 0.18 0 6.54 2 0.46 0 8.62 5 3.51 3

KPSS Test 5% Critica l Value

La g

Test

5% Critical Value

-1.943

8

a

0.091

0.463

-3.444

9

b

0.347

0.146

-3.444

0

b

0.160

0.146

-3.444

9

b

0.154

0.146

-1.943

5

b

0.072

0.146

-3.444

9

b

0.259

0.146

-1.943

6

b

0.072

0.146

-1.943

9

a

0.207

0.463

-1.943

4

a

0.313

0.463

-3.444

8

b

0.253

0.146

2

a

0.149

0.463

-3.444

8

a

0.154

0.463

-1.943

5

b

0.160

0.146

-1.943 -3.444

3

b

-1.943

5

c

1.55 2 8.59 7

Note: ADF - the final choice of lag was made based on Schwarz criterion. PP and KPSS tests - lag is the lag truncation chosen for the Bartlett kernel. “a” denotes intercept; “b” denotes intercept and trend, and; “c” denotes none.

Table 3 – OLS and GMM estimates (2005M01 to 2015M12). Dependent

Equation OLS

Variable: RP

Eq 5

c

ΔExpect_GDP48

Δinfl

ΔExpect_ND

0.051

0.053

0.002

0.002

-0.013

-0.036

-0.144

Eq 8 0.166**

(0.246)

(0.244)

(0.224)

(0.226)

(0.106)

(0.101)

(0.089)

(0.079)

[0.209]

[0.219]

[0.011]

[0.009]

[-0.124]

[-0.351]

[-1.624]

[-2.101]

2.554

2.878

3.183

3.206

7.376***

8.432***

8.139***

8.446***

(2.057)

(2.010)

(1.945)

(1.998)

(2.333)

(2.339)

(1.549)

(1.460)

[1.241]

[1.432]

[1.637]

[1.604]

[3.162]

[3.605]

[5.253]

[5.784]

0.711

0.563

0.605

0.586

1.404***

1.165***

1.333***

1.462***

(0.762)

(0.737)

(0.715)

(0.673)

(0.341)

(0.379)

(0.372)

(0.345)

[0.933]

[0.764]

[0.846]

[0.87]

[4.121]

[3.074]

[3.582]

[4.237]

3.464**

3.343***

2.817***

2.819***

7.025***

6.7***

5.055***

5.095***

(1.391)

(1.266)

(0.926)

(0.943)

(0.663)

(0.745)

(0.672)

(0.750)

[2.491]

[2.64]

[3.043]

[2.989]

[10.592]

[8.994]

[7.524]

[6.79]

ΔEmbi

Eq 6

Equation GMM Eq 7

Eq 8

Eq 5

Eq 6

Eq 7

0.769

0.718*

0.715*

0.941**

0.765*

0.681*

(0.496)

(0.368)

(0.364)

(0.471)

(0.394)

(0.372)

[1.55]

[1.948]

[1.962]

[2]

[1.94]

[1.828]

0.666

0.666

1.416***

1.527***

(0.407)

(0.407)

(0.157)

(0.134)

[1.639]

[1.637]

[9.021]

[11.434]

ΔDisag_ND

ΔCredib

-0.366

-2.042*

(2.443)

(1.071)

[-0.15]

[-1.907]

R-squared

0.108

0.128

0.189

0.189

0.082

0.104

0.125

0.104

Adj R-squared

0.087

0.101

0.156

0.150

0.058

0.072

0.085

0.056

F-statistic

5.147

4.638

5.809

4.813

Prob F-statistic

0.002

0.002

0.000

0.000

J-STAT

18.614

17.385

18.610

19.019

p-value (J-STAT)

0.910

0.921

0.948

0.966

Rank

32

32

36

39

Notes: Marginal Significance Levels: *** denotes 0.01, ** denotes 0.05 and *10%. Standard errors in parentheses and t-statistics in square brackets. Regarding OLS estimates, due to the problems of autocorrelation and heteroskedasticity (Table A.1 in the Appendix shows the residual diagnostics tests), the reported t-statistics in the OLS estimates are based on the estimator of Newey and West (1987). GMM Instruments: Eq 8: RP(-1 to -2) ∆Expect_GDP48(-1) ∆Infl(-1 to -13) ∆Expect_ND(-1 to -2) ∆embi(-1 to -7) ∆Disag_ND(-1 to -8) ∆Credib(-1 to -5). Eq 7: RP(-1 to -2) ∆Expect_GDP48(-1) ∆Infl(-1 to -14) ∆Expect_ND(-1 to -2) ∆embi(-1 to -5) ∆Disag_ND(-1 to -8) ∆Credib(-1 to -3). Eq 6: RP(-1 to -2) ∆Expect_GDP48(-1) ∆Infl(-1 to -14) ∆Expect_ND(-1) ∆embi(-1 to -6) ∆Credib(-1 to -7). Eq 5: RP(-1 to -2) ∆Expect_GDP48(-1) ∆Infl(-1 to -14) ∆Expect_ND(-1) ∆embi(-1 to -6) ∆Credib(-1 to -7).

Table 4 – ARDL – Inflation risk premium long run coefficients RP - ARDL(8, 8, 4, 6, 8, 7, 7) Critical bounds

Bounds test Test statistic

Value

Significance

II Bound

F-statistic

7.216

5%

3.61

K

6

1%

4.43

value

Long run coefficients Variables

Coefficient

Std. Error

t-statistic

Expect_GDP48

1.315***

0.396

4.239

Infl

0.436***

0.135

3.928

Embi

0.019

0.193

3.623

Expect_ND

0.405**

0.163

3.992

Disag_ND

0.868***

0.150

4.046

Credib

-3.272**

1.448

1.541

c

-4.621***

0.902

0.327

Notes: Marginal Significance Levels: *** denotes 0.01, ** denotes 0.05 and *10%. Standard errors in parentheses and t-statistics in square brackets.

Appendix A Table A.1 - Correlation between daily disagreement measures in fixed events forecast Correlation Year

\ 2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

Disag_NDt, SD(ND)

0.960

0.977

0.972

0.965

0.772

0.810

0.906

0.912

0.880

0.930

0.925

Disag_NDt, CV(ND)

0.956

0.975

0.973

0.959

0.762

0.831

0.881

0.887

0.839

0.951

0.896

Obs

1039

1222

1227

1211

1245

1233

1233

1235

1237

1237

1234

Disag_NDt is the disagreement methodology used in this work, SD(ND) is the standard deviation and CV(ND) is the coefficient of variation of the daily distribution released by the Brazilian Central Bank. Each cells inform the correlation between the measures of disagreement in expectations, which are formed for the closure of the year informed in the heading of the table.

Table A.2 - Correlation between monthly disagreement measures in fixed events forecast Correlation Year

\ 2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

Disag_NDt, SD(ND)

0.964

0.981

0.960

0.956

0.749

0.771

0.917

0.927

0.819

0.936

0.931

Disag_NDt, CV(ND)

0.960

0.979

0.960

0.950

0.730

0.819

0.892

0.902

0.773

0.959

0.903

Obs

41

53

60

59

60

60

59

59

60

59

59

Disag_NDt is the disagreement methodology used in this work, SD(ND) is the standard deviation and CV(ND) is the coefficient of variation of the monthly average of the daily distribution released by the Brazilian Central Bank. Each cells inform the correlation between the measures of disagreement in expectations, which are formed for the closure of the year informed in the heading of the table.

Appendix B Table B.1 – Residual diagnostics tests for OLS regressions in Table 3 Eq 5

Eq 6

Eq 7

Eq 8

LM(1) test

263.3

239.5

112.6

112.4

Prob. LM(1) test

0.000

0.000

0.000

0.000

LM(2) test

131.7

118.9

64.5

64.8

Prob. LM(2) test

0.000

0.000

0.000

0.000

ARCH(1) test Prob. ARCH(1) test ARCH(2) test Prob. ARCH(2) test Jarque-Bera Prob. JarqueBera

235.4

255.6

185.7

186.2

0.000

0.000

0.000

0.000

128.362

146.238

64.532

92.770

0.000

0.000

0.000

0.000

66.972

57.029

30.593

30.435

0.000

0.000

0.000

0.000