The communication effects on inflation forecast errors: Empirical evidence from Colombia

The purpose of this article is to explore the central bank's ability to
 management inflation forecast errors in Colombia. We present empirical
 evidence based on the Colombian experience with data from the period of 2008
 to 2020. The communication channel selected for analysis is the press
 releases. The empirical evidence is divided into three steps: (i) regression
 analysis using an EGARCH model, (ii) use of VAR models, and (iii) variance
 decomposition analysis. The communications effects are significant for
 several months and that close to half of the forecast error variance can be
 explained by innovations in central bank communication. The results obtained
 allow monetary policymakers to develop more efficient strategies for
 anchoring expectations and strengthening the central bank credibility.


Introduction
Inflation expectation management is fundamental for monetary policy credibility and macroeconomic performance (David Johnson, 2003;Michael Ehrmann et al., 2011;Michael Scharnagl and Jelena Stapf, 2015). In inflation targeting, the central bank has different tools to improve transparency and reduce asymmetric information in the financial market. As a result, market inflation forecasts are more accurate (Ben Bernanke et al., 1999;Petra Geraats, 2002;Christopher Crowe, 2010).
There is a need to broaden the research on the communication effects on controlling financial market expectations in emerging economies. This study helps to understand how the central bank communication affects inflation forecast errors and it contributes to the literature in several ways. First, in accordance with the methodology applied by Mankiw, Reis and Wolfers (2004) and Pedersen (2015), it demonstrates that monetary policy announcements have significant effects on forecast errors. Second, it analyzes the Colombian economy, an economy with a gap in the literature in terms of the possible effects of communication on controlling financial market inflation expectations. Third, it provides evidence that the bank's announcements have the potential to decrease inflation forecast errors.
We choose the Colombian economy because it is an emerging economy that adopted inflation targeting in the year 2000, and the Central Bank of Colombia has perfected his communication channels with the public. In addition, it has investment grade, and the development of the capital market is based on the growth of the domestic public debt market. In short, it is worthwhile to analyze inflation forecast errors in the Colombian context.
The remainder of this article is structured as follows: section 2 makes a brief presentation of the monetary history of Colombia; section 3 makes a literature review; section 4 defines the inflation forecast error and presents the methodology for measuring the effects of communication on forecast errors; section 5 provides econometric estimates and a discussion of the results obtained; section 6 concludes the article.
The bank's institutional principles were modified in 1991, and since then, its main objective has been to maintain a low and stable inflation rate. For this, the board of directors was modified to be independent of the economic sectors. 3 Since then, the bank's board of directors has been made up of seven members: the minister of finance and public credit; five permanent members, appointed for 4 years; and the general manager.
Since 2000, the Central Bank of Colombia adopted the inflation targeting regime and inflation rates have averaged 5% per year. For this, the bank has the commitment to announce an inflation target each year and the responsibility for its compliance. Furthermore, from 2003, the announcement of the target is accompanied by the announcement of tolerance intervals that allow monetary policy to adjust less severely to external shocks (Enrique López-Enciso, Hernando Vargas-Herrera and Norberto Rodríguez-Niño, 2016).
The bank pursues its policy objectives through open market operations, discounted loans, and reserve requirements. The main control variable is the monetary policy interest rate or intervention rate (López-Enciso et al., 2016). However, the most widely used policy tool is open market operations, which consist of buying or selling public debt securities of the Colombian government.
The bank's objectives and their strategies, economic prospects, and future decisions are systematically announced since the late 1990s (Juan Anzoátegui and Juan Galvis, 2019). Since 1997, the general manager presents two annual reports to the Congress of the Republic on the execution of monetary policy. Moreover, from 2000, decisions on the policy rate have been announced through press releases. In addition, since 2012, the policy decision is presented to the media at a press conference. From 2007, the minutes of the decisions on the policy rate have been published. In the minutes, the inflationary situation and the prospects for the economy are discussed. In addition, these are presented with the details of the economic information that was used to make decisions about the interest rate. With regard to decision-making meetings, policy decisions between 2000 and 2017 were made monthly. As of 2018, eight meetings are held; this is to maintain synchrony with the monetary policy decisions made by the main central banks in the world.

Short Review of Literature
The literature presents results linking the central bank's communication with the performance of monetary policy, term structure of interest rates, and managing inflation expectations (Michael Woodford, 2005;Alan Blinder et al., 2008;Michael Ehrmann and David Sonderman, 2012). Thus far, the findings denote that different communication channels of the central banks (Press Releases, Statements, Inflation Reports, Minutes, Interviews, Records, Financial Reports, etc.) contains fundamental information affecting the financial markets' performance and economic outlook.
Several studies have evaluated the communication effect on market expectations. Between these, Carlo Rosa and Giovanni Verga (2007) found that the surprise component of the Statements of the European Central Bank affects future contracts, and the European Central Bank is effective in its communication to the public because influences market expectations on the short-term interest rate path. Also, Rachel Reves and Michael Sawicki (2007), Ehrmann and Sonderman (2012) found that interest rate expectations respond to the surprise component contained in the Inflation Reports and Minutes. In the case of emerging economics, Gabriel Montes et al. (2016) shows that the monetary policy signaling and the minutes of the COPOM-Brazil reduces heterogeneity in inflation expectations.
In this study, we defined the forecast error as the difference between the market inflation forecast and the central bank's inflation target. Thus, the forecast error is a measurement associated with the credibility of monetary policy. To our knowledge, no studies have been done to research the effects of communication on forecast errors based on the inflation expectations implicit in government bonds in emerging economies. This article aims to fill this gap in the literature.

Methodology and data
A well-anchored inflation expectation in the inflation targets is fundamental to the central bank because it indicates the public confidence on monetary policy (Refet Gürkaynak, Andrew Levin, and Eric Swanson, 2010;Andrew Levin, 2014). Inflation forecast errors reflect disagreements among agents with regard to the monetary policy management. Consequently, a reduction in market forecast errors contributes to inflation control and financial system stability (Mankiw, Reis, and Wolfers 2004).
Transparency and communication are important central bank tools for reducing bias and anchoring inflation expectations into target (Ehrmann, Eijffinger, and Fratzscher, 2012). In emerging economies, there are several sources of uncertainty and external shock that make it difficult to control expectations (Michiel De Pooter et al., 2014). Specifically, it is difficult for markets to anticipate the decisions of the central bank, and these include surprise elements (Tore Ellingsen and Ulf Söderström, 2001). The main objective of this study is to analyze the effect of monetary policy announcements on the anchoring of inflation expectations in the Colombian economy. The results obtained allow monetary policymakers to develop more efficient strategies for anchoring expectations and strengthening the credibility of the central bank.
To calculate the behavior of agents' expectations, we use market-based estimates, which have proved better predictors than estimates based on surveys. The measures derived from the assets prices are available daily and reveal an accurate projection of the investors' expectations for inflation (Ian Christensen, Fréderic Dion, and Christopher Reid, 2004;Refet Gürkaynak, Brian Sack, and Eric Swanson, 2005;Paul Söderlind, 2011).
The most popular market measurement used to estimate inflation expectations is Break-Even Inflation (BEI), also known as inflation compensation (Gürkaynak et al., 2010 andSöderlind, 2010). The BEI captures the compensation that investors demand both for expected inflation and for the risks or uncertainty associated. Therefore, BEI is a measurement of inflation expectations and is calculated as the inflation rate at which investors will have no preference between nominal and inflation-indexed bonds. That is, where is the inflation expectations or BEI, , is the nominal bond yields, , is the index-linked bond yields and is the maturity period of the bond.
Based on monthly data, the behavior of inflation expectations over time (BEI) and the inflation target are presented in Figure 1. In general, it is observed that market expectations closely follow the target set by the Central Bank of Colombia. It is possible to identify deviations above the goal, which indicate a de-anchoring of expectations in 2008 related to the uncertainty and great slowdown generated by the subprime crisis and between 2015 and 2017 caused by the fall in oil prices. In turn, there are deviations below the goal, which occurred between 2009-2010 and 2012-2014, which indicate an important control of expectations. In short, the inflation target has the ability to guide the expectations of the financial market. The BEI has proved efficient in measuring short-term inflation expectations for Colombian economy (Melo and Granados, 2010). As such, we used bonds with a maturity period of one year in this study to calculate inflation expectations. Both positive and negative deviations from the target are considered to be errors (Johnson, 2003 andMankiw, Reis andWolfers, 2004). Thus, the forecast error is constructed as the difference between the inflation target and inflation expectations, thus:

Figure 1 Inflation expectations and inflation target
where is the forecast error, * is the inflation target and are the inflation expectations. The error can take positive values * > that indicate anchoring of expectations and can take negative values * < that signal loss of control of expectations by the bank. Therefore, the sign of the deviations is important because it allows us to identify the monetary policy reaction, for example, when the error takes negative values. The behavior of forecast errors for the Colombian economy during the period of 2008 to 2020 are presented below (see Figure 2). 4 On average, the forecast error in Colombia was -0.084% (see Figure 2). In general, the forecast error is positive in a large part of the analyzed sample. This means that inflation expectations converged to the central inflation target when it was set at 3% (from 2010 onward). However, the error remains on the downside significantly from 2015 to the end of 2017 resulting in an average forecast error of -1.061% when inflation expectations accelerated.

Figure 2
Forecast error evolution in Colombia Overall, central bank decisions involve both expected and unexpected components.
The expected component has already been incorporated into agents' expectations and does not have significant effects on markets (Alan Blinder et al., 2008). As such, to analyze the effects of communication special attention must be paid to the unexpected component (David-Jan Jansen and Jakob De Haan, 2007;Gürkaynak et al., 2010;Ehrmann et al., 2011).
The surprise element in monetary policy is the unexpected component in central bank communication and appears when agents do not anticipate the behavior of the interest rate because they do not understand the monetary policy posture. Unexpected changes are linked to information asymmetry, where the central bank possessed information not known by the public. Consequently, surprises cause some disruption in the financial market and affect the anchoring of inflation expectations to the inflation target; therefore, communication has an impact on forecast errors (Andre Filardo andDiwa Guinigundo, 2008 andGabriel Montes et al., 2016).
In accordance with the methodology proposed by Kuttner (2001) and Connolly and Kohler (2004), the unexpected component is defined as the change in the 30-day interest rate on the day of central bank announcement. The 30-day interest rate reflect market expectations on monetary policy decisions. Therefore, these rates vary according to the extent that agents are caught off guard in terms of the expected monetary policy position (see, for example, Kenneth Kuttner, 2001). In Colombia, according to Juan Galvis and Juan Anzoátegui (2017)  The IBR reflects the short-term liquidity position that the banks expect and is a result of stock market negotiation in the Colombian financial system. 5 Thus, to calculate the surprises in the Central Bank of Colombia announcements, we calculated the changes in IBR rate: where is the unexpected component of monetary policy announcements and ∆ is the IBR change between t and t-1, and t is the announcement day. To calculate the unexpected component, we focus on press releases which are published monthly immediately after a meeting of the board of directors. This channel receives much attention from financial markets and enable quick identification of changes in monetary policy stance. The press releases provide to the public is concrete information, and the main objective is to briefly report the basic reasons behind each decision of monetary policy intervention rate.
The changes in the IBR rate on the press releases days are presented in Figure 3. The dates on which the central bank communicates its decisions were set according to the calendar provided by the board of directors of the Central Bank of Colombia. 6 Whenever a press release came out after the closing of the Colombian stock market, the day of the press release was recorded as the next business day. In Figure 3, the changes in the IBR rate shows that the market reacts to the press releases, which suggests that each decision made by the central bank has unexpected components and effects on the financial market. The changes in the IBR rate imply divergences in market expectations and affect forecasts for future intentions with regard to monetary policy stance. In turn, unexpected variations in the policy rate lead investors to revalue expected returns on nominal and indexed bonds. Thus, when the financial market reacts to monetary policy decisions, it is expected a rearrangement of inflation expectations in relation to the central bank's targets. According to Mankiw, Reis, and Wolfers (2004), it is also important to point out that the forecast error demonstrates significant inertia over time. Therefore, we used the following basic model: where is the forecast error and −1 is the forecast error in the past period and captures the inertia in the forecast error. The term is the unanticipated component of monetary policy, and X i is a vector of control variables.
The residual term is u t = v t h t~( 0, h t 2 ), with v t = u t h t~i id(0,1). We assumed that the residual term has a conditional variance with the following process: To improve the efficiency in estimation [4], we assume that the residuals can be modelled as an EGARCH (2,2). According to Robert Engle (1982), GARCH conditional variance models are useful because they consider the features of the series derived from the financial market, which usually have non-normal distribution and show a high kurtosis. Specifically, the EGARCH or exponential GARCH model was proposed by Daniel Nelson (1991) and is advantageous because it differentiates between the asymmetrical effects of the changes on inflation forecast errors from positive or negative shocks.
According to Mankiw, Reis, and Wolfers (2004) and Apergis (2017), forecast errors are also affected by other variables not related to monetary policy decisions. There are evidences that exchange rate variations affect inflation expectations in the Colombian economy (Hernán Rincón and Norberto Rodríguez, 2017). Therefore, as a first control variable, we used nominal exchange rate variations (∆e).
The global financial uncertainty is an important factor in capital flows to emerging economies because the changes in international market contribute to asset prices volatility and as a result, affect inflation compensation (Joseph Byrne and Norbert Fiess, 2016). One indicator that measures investors' appetite for risk is the S&P 500 Market Index or VIX Index, which signals the global risk of capital flows. Thus, the second control variable is the VIX Index variation (∆VIX).
The interest rate for US bonds reflects global economic conditions and functions as a proxy for the risk-free interest rate. In addition, global liquidity is a standard variable for any investor and the interest rate for US Treasury bonds reflects the international cost of capital and affects returns on the sovereign bonds of domestic economies (Martin González-Rozada and Eduardo Levy-Yeyati, 2008). Consequently, the third variable is the interest rate for US Treasury bonds (∆i*).
In emerging economies, there is a significant pass-through of oil prices to domestic prices. In addition, the price of oil greatly influences the macroeconomic stability of the Colombian economy. Specifically, the oil price volatility also influences returns on nominal and indexed public bonds and as such, on inflation compensation (Diego Martínez, José Moreno y Juan Rojas, 2015). Thus, we used the oil prices changes (∆OIL) as the fourth control variable.
To sum up, together with unanticipated component of monetary policy, four control variables are considered (∆e, ∆VIX, ∆i*, ∆OIL). To standardize the measurement units for the different control variables, we used standard deviation and this is calculated on the press release days (see, for example, Gürkaynak et al., 2010;Ehrmann et al., 2011;De Pooter et al., 2014).
We used data from January 2008 to March 2020. The source and descriptive statistics of all variables can be found in the Appendix (Tables A.1 and A.2). The first procedure to be carried in time series is verifying the existence of unit roots. Therefore, before estimating of the models, the following tests were performed: the augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests. The results denote that all series are I(0) (see Table A.3, Appendix).

Empirical Evidence
We present baseline empirical results in Table 1. First, the basic model that evaluates the effect of communication on inflation forecast errors is estimated, and then the base model is expanded, and all control variables are added at once.
An initial inspection of the coefficients associated with communication show that the sign is in line with the expected theoretical perspective, and the estimated parameters are significant. The central bank has more and better information about the economic performance. Consequently, when the central bank makes announcements, it reduces the level of uncertainty in the financial system, and the market adjusts its forecast according to the newly outlined prospects (Pedersen, 2015). The results show that the coefficient associated with monetary policy announcements has, in statistical terms, opposite and significant effects on forecast errors in all estimated models. Overall, the evidence suggests that announcements decrease the forecast error, and as such, it can be inferred that the central bank has the capacity to cause inflation expectations to converge to the target. Similar results have been reached by Pedersen (2015), Dräger and Lamla (2012), and Johnson (2003).
The financial variables also affect the market forecast errors. In general, the signs of the variables' coefficients are in line with the expectations, and the coefficients are significant in the estimated models. The forecast error shows persistence because in the market, agents take some time to understand the business cycle (Mankiw, Reis and Wolfers, 2004). According to the results, the estimates show that the lag in the forecast error ( −1 ) is positive with a significance level of 1% in all models. Thus, the lag is important and help to explain financial market forecast errors. A similar result is reported by Mankiw, Reis, and Wolfers (2004) and Jan Babecký and Jiri Podpiera (2011).
The parameter associated with the exchange rate (∆e) is positive and significant. The exchange rate increases have a significant pass-through to domestic prices in Colombia (Rincón and Rodríguez, 2017). As a result, the exchange rate puts pressure on inflation expectations, thereby affecting forecast errors. Similar results are found by Siklos (2008), Pedersen (2015) and Apergis (2017).
Estimates resulting from oil price changes(∆OIL) show that the coefficient is positive with a significance level of 1% and is reinforced by empirical literature, which suggests oil price effects on inflation forecast errors (see Pedersen, 2015;Fréderique Bec and Annabelle De Gaye, 2016). In addition, the parameter associated with the external interest rate (∆i*) is positive and significant in statistical terms. Thus, an increase in the external interest rate leads to a rise in forecast errors because of the potential effects on the movement of capital and the exchange rate. Finally, with regard to the (ΔVIX) coefficient, the results are in line with the literature. The coefficient is positive, which shows that the global risk-measured by the VIX index-moves the financial markets of emerging economies, affects expectations, and influences the forecast error (see De Pooter et al., 2014).

Asymmetric effects of central bank communication
This section verifies the existence of asymmetric effects in the central bank's communication. In general, central banks increase their efforts to improve their communication in situations of great uncertainty that desanchoring inflation expectations (Bernd Hayo, Ali Kutan and Matthias Neuenkirch, 2015).  Table 2 shows the results of the regressions carried out to identify the effects of communication when errors are positive and negative. The results found allow identifying the existence of asymmetric effects in communication. We found evidence that the coefficient associated with communication (MPS) is higher when the error is negative, that is, when there is a de-anchoring of expectations.
The empirical literature suggests that the uncertainty associated with unexpected changes in macroeconomic fundamentals increases the risk for investors. In particular, the drops in expectations below the inflation target suggest economic recessions, when errors tend to be negative. In this situation, two reactions coincide: (i) agents pay more attention to monetary policy decisions to reduce uncertainty and (ii) central banks are concerned with providing more information, and this amplifies the effects of communication on the financial market (Benjamin Born, Michael Ehrman and Marcel Fratzscher, 2013).

Impulse Response and Variance Decomposition
With the aim of increasing the evidence that central bank announcements influence inflation forecast errors, we extend our analysis through a vector autoregressive (VAR) model. As usual, the dynamics analysis is carried out using impulse-response functions because they offer the possibility of observing the effect of an impulse in the communication caused by shocks or innovations. In accordance with Gary Koop, Hashem Pesaran and Simon Potter (1996) and Hashem Pesaran and Yongcheol Shin (1998), we used a generalized impulse-response function as it is invariant to the order of the variables considered in the VAR. Note: Accumulated response to a generalized s.d. innovation ± 2 S.E.
The impulse-response analysis is performed for the variables, and . The order of the VAR lag is chosen based on the Hannan-Quinn information criterion (HQC), which is consistent for small samples (see Table A.4 in the Appendix). Figure 4 shows the results of the generalized impulse-response function for a period of 12 months. The graphic suggests that an unexpected positive shock caused by an announcement provokes a significant reduction in forecast errors starting in the second month. In addition, the impact is significant up until month 10. In brief, Central Bank of Colombia announcements aid in reducing bias in financial market expectations.
To complement the impulse-response analysis, a variance decomposition is carried out below. The variance decomposition of forecast errors in the event of an innovation in communication and an innovation in forecast errors is presented in Table 3. As shown, an innovation in the central bank's communication accounts for nearly 2.6% of the forecast errors variation in the second period. The impact of the announcement increases monotonously, and at the end of month 12 explains 19.6% of the forecast errors variance. In short, the evidence suggests that communication must be considered when analyzing inflation forecast errors in the financial market.

Concluding remarks
In this article, we study the impact of Central Bank of Colombia announcements on inflation forecast errors for the Colombian economy. Inflation expectations were extracted from government bonds, and the forecast error was calculated based on the difference between inflation expectations and the inflation target. In addition, the effects of the central bank's announcements on the forecast error were captured through the unexpected components of monetary policy decisions. Following the construction of the variables, econometric estimates were carried out.
The results allow three observations. First, communication from the Central Bank of Colombia is a monetary policy tool that promotes convergence between financial market expectations and the inflation targets. Consequently, communication proves effective in managing expectations.
Second, the impulse-response analysis shows that communication reduces the forecast error and that its effects are significant for several months. In addition, the variance decomposition analysis confirms that close to half of the forecast error variance can be explained by innovations in central bank communication. Thus, the evidence that has been presented shows that there is a channel of expectations, given that the central bank has the capacity to make expectations converge toward the inflation target.
Third, and finally, there are other variables not related to communication that affect the inflation expectations management. One such variable is the forecast error persistence. Other factors include the exchange market volatility, global uncertainty, and the monetary policy of the US Federal Reserve. These factors are shown to have effects on forecast error and have the potential to deviate market expectations from the inflation target.   Note: HQC: Hannan-Quinn information criterion. a Indicates lag order chosen by criterion. Figure 1A -VAR Stability