Monetary policy and inflation expectations in Brazil: From 2005 to 2022

Alencar, Douglas Alcântara; Pereira, Wallace Marcelino; Lima, Andressa; Caldas, Lucas Article Monetary policy and inflation expectations in Brazil: From 2005 to 2022 Journal of Business and Economic Studies (JBES) Provided in Cooperation with: Northeast Business and Economics Association (NBEA) Suggested Citation: Alencar, Douglas Alcântara; Pereira, Wallace Marcelino; Lima, Andressa; Caldas, Lucas (2024) : Monetary policy and inflation expectations in Brazil: From 2005 to 2022, Journal of Business and Economic Studies (JBES), ISSN 2576-3458, Northeast Business and Economics Association (NBEA), Port Jefferson, NY, Vol. 28, Iss. 2, pp. 1-17 This Version is available at: https://hdl.handle.net/10419/333860 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-sa/4.0/ Journal of Business and Economic Studies Vol. 28 Issue 2 Monetary Policy and Inflation Expectations in Brazil: From 2005 to 2022 Douglas Alencar Federal University of Pará E-mail: [email protected] Wallace Pereira Federal University of Pará E-mail: [email protected] Andressa Lima Federal University of Pará E-mail: [email protected] Lucas Caldas Federal University of Pará E-mail: [email protected] Abstract The Focus Report prepared by the Central Bank of Brazil summarizes the statistics calculated from market expectations, such as inflation expectations for the next four years that are weekly collected. The report shows the evolution of these data using graphs and weekly projections for price indices, economic activity, and exchange rates. However, the expectations of households and firms regarding the future of inflation, which are determinants for current inflation, go beyond problems of theoretical and empirical foundation. Thus, the research question addressed in this study is as follows: Do expectations of inflation measured by the Focus Market Report explain inflation measured by the CPI in Brazil? To answer this question, we compare expected and actual inflation data and analyze the correlations between them. This research is important because part of the argument for increasing the basic interest rate in the Brazilian economy is based on data from the Focus Report, which may contain forecasting errors, thereby resulting in monetary policy mistakes. The research methodology consists of contrasting data on monthly expectations with actual inflation rates and assessing the correlations between them. Keywords: monetary policy, inflation, expectations, Focus Market Report, Brazil JEL codes: E12, E52 1. Introduction The theoretical models developed by Phelps, Friedman, and Lucas are capable of intuitively demonstrating that expected inflation plays a fundamental role in the inflationary trajectory. The underlying reasons lie in the assumptions of the persistent monetary illusion and microfoundations, which are particularly grounded in the concept of price rigidity. This framework underpins the monetary policy in various economies worldwide (Rudd 2022). The implications for economic policy management are that, based on expectations, the monetary authority can project future inflation and monitor the ability to combat sharp price fluctuations in line with the central objective. This theoretical framework plays a central role D. Alencar, W. Pereira, A. Lima, L. Caldas 2 in shaping expectations regarding inflation without necessarily explaining the constitutive elements in detail. Neither the optimal measurement method nor the agents to be consulted are discussed. Furthermore, whether expectations exhibit a uniform pattern and can affect inflation dynamics in any type of economy is not explored. For example, the Focus Report prepared by the Central Bank of Brazil summarizes statistics calculated based on market expectations. Notably, the report highlights inflation expectations for the next four years collected weekly. This report illustrates the evolution of these data, such as through graphs and weekly projections of price indices, economic activity, and exchange rates. As Rudd (2022) argues, the expectations of households and businesses regarding future inflation are among the main determinants of actual inflation. However, these expectations, which are crucial for current inflation, go beyond theoretical and empirical foundations. Thus, this study explores the following research question: Do inflation expectations measured by the Focus Market Report explain inflation measured taken by the IPCA (Broad National Consumer Price Index) in Brazil? Therefore, this study assesses the impact of expectations, as measured by the Focus Market Report, on actual inflation, as measured by the official Brazilian price index. We compare expected and actual inflation data and analyze the correlations between them. This study is important because part of the argument in favor of raising the basic interest rate in the Brazilian economy relies on data from the Focus Report, which may contain prediction errors, potentially leading to misguided monetary policies. According to Vereda et al. (2020), between 2001 and 2019, the credibility of the monetary authority oscillated between two opposing poles. Deterioration was continuous between mid-2007 and 2016, at which point credibility was regained and has been retained since. The remainder of this paper is organized as follows. Section 2 focuses on inflation expectations, while Section 3 presents historical context for the monetary policy in Brazil from 2005 to 2022. Section 4 presents an empirical exercise used to test the hypothesis that inflation expectations affect official inflation in Brazil. Finally, Section 5 provides the study’s conclusions. 2. Inflation Expectations Considering the New Keynesian approach and, therefore, the inflation targeting model, the Phillips Curve in its accelerationist version is significant for understanding central bank actions regarding interest rates. In this section, we discuss the key aspects of the Phillips Curve, particularly in terms of its accelerationist version. As Rudd (2022), Carlin and Sosckice (2005), and Arestis (2011) have shown, the variable of expectations regarding future inflation is a crucial component of the New Economic Consensus and New Keynesian models. Expectations regarding future inflation appear in the monetarist version of the Phillips Curve and are retained in the New Keynesian model. Central banks have embraced this, arguing that inflation expectations affect current inflation. Thus, central banks assess whether inflation expectations for the future align with inflation targets. If the expectations do not point towards the inflation target, the central bank attempts to anchor expectations by increasing the interest rate. The Phillips Curve is based on the pioneering work published by A.W. Phillips in 1958. It addresses the inverse relationship between the inflation rate and unemployment, allowing a tradeoff to be established between these two variables (Figure 1). To illustrate the application of the Phillips Curve, let us assume an increase in the money supply from 3% to 5% (a 2% increase), which, consequently, will lead to an increase in aggregate demand and a subsequent rise in nominal wages. D. Alencar, W. Pereira, A. Lima, L. Caldas 3 According to Friedman (1968), an increase in income leads to a reduction in the unemployment rate because more individuals accept the offered nominal wages. The output of the economy responds to the growth in aggregate demand, compelling producers to augment their employee numbers, production, and working hours. This surge in aggregate demand also exerts an upward pressure on prices, thereby increasing the inflation rate. Thus, low unemployment rates signify increased inflation, whereas high unemployment rates diminish this effect. Figure 1 – Phillips Curve (CP) As Figure 1 above illustrates, at an inflation rate of zero, the unemployment rate is 6%. Moving along the curve, a 4% unemployment rate increases the inflation rate by 2%, demonstrating a trade-off between unemployment and inflation. According to Friedman, an increase in employment is only possible because agents have set wages and prices for the future, making it take some time for labor suppliers to realize that prices have risen more than nominal wages (i.e., real wages have not decreased). However, this model operates only in the short term. In the long term, the adaptive expectations hypothesis posits that individuals adjust their expectations to prevent repeating past errors. Therefore, if in a previous period, labor suppliers underestimated inflation in the subsequent period, they adapted their expectations by incorporating previously acknowledged expectations. Thus, the equation is as follows: 𝜋𝑡 𝑒 = 𝜋𝑡−1 𝑒+ β (𝜋𝑡−1𝜋𝑡−1 𝑒) (1) where β is the speed of corrections to expectations. If we consider that β = 1, the result of the equation will be 𝜋𝑡 𝑒 = 𝜋𝑡−1. This demonstrates that labor suppliers assume that analyzing the past is the most effective method for speculating about the present and future. Therefore, for inflation to decrease, a deflationary shock becomes necessary, causing unemployment to rise at a rate above the natural rate and pressuring individuals to revise their expectations. D. Alencar, W. Pereira, A. Lima, L. Caldas 4 Thus, the Phillips Curve can be considered to become vertical in the long term as soon as agents anticipate the process of price increases, which demands higher real wages (Figure 2). Consequently, higher inflation and unemployment will return to their natural rates. Even if economic policymakers attempt to fix employment at a level lower than the natural rate by increasing the money supply, agents' expectations will always shift the curve upward and to the right until decision-makers realize that inflation has become a more serious problem than unemployment. Figure 2 - Augmented Phillips Curve In this scenario, actions to contain inflation by increasing unemployment do not have immediate effects. Similar to individuals taking some time to realize that real wages have decreased, it takes time for them to recognize that the inflation rate has decreased and accept lower nominal wages. The theoretical models of Phelps, Friedman, Lucas, Rapping, and the post-Keynesians highlight the importance of considering expected inflation as a key determinant of actual inflation. These arguments contribute to explaining the Phillips Curve and inflationary experiments from 1960 to 1980 in the United States. The full utilization of these economists' theoretical models has policy implications. According to Rudd (2022), for an inflation analyst, expected inflation measures can explain the evolution of past inflation and project inflation measures. For a monetary authority such as the Central Bank, successfully controlling inflation expectations is fulfilling its objectives. Edmund Phelps' model states that the intercept of the Phillips Curve would shift oneto-one with expected inflation, as labor supply would be independent of the interest rate and, consequently, independent of expected inflation. Thus, according to Phelps (1967), nominal variables do not permanently affect real variables. Therefore, Phelps's model ignores the consequences that anticipation of inflation may have on current real income. However, Friedman (1968) has asserted that labor suppliers accept work based on expost real wages. Labor suppliers would take some time to perceive an increase in general price D. Alencar, W. Pereira, A. Lima, L. Caldas 5 levels. In this model, increased employment is possible only when prices increase, thereby reducing real wages. However, when workers anticipate price increases, the result is reflected in nominal wages, leaving real wages unchanged. According to Rudd (2022), the theories of both Phelps and Friedman consider that nominal disturbances cannot have permanent real effects on the economy and that the market will always return to its natural equilibrium. Furthermore, both theories assert the existence of a real side of the economy that exerts its influence, regardless of nominal variations. Fisher (1983) criticizes this, stating that no convincing evidence exists on the stability of economic equilibrium. According to Friedman's derivation of the Phillips Curve, wages are countercyclical and companies are always on their demand curve. For Friedman, the selling prices of products react more quickly than wages. However, US data have shown that wages are procyclical because conventional equations indicate that the trade-off between wage inflation and employment is more pronounced than price inflation. Lucas and Rapping have proposed another theory that emphasizes the relationship between expected and real inflation. In their model, real (expected) interest rates affect the current labor supply, thereby influencing the tradeoff between goods and leisure. The model also reinforces the existence of adaptive expectations and one-to-one adjustments in nominal interest rates. This model assumes that an increase in the current inflation rate will increase the expected inflation rate, which is valid only through a specific formulation of adaptive expectations. This assumption suggests that inflation converges to a steady state. Furthermore, significant employment fluctuations cannot be assumed without correspondingly large intertemporal substitution fluctuations. In 1973, Lucas developed a model to analyze market prices and determine whether a specific price disturbance was an absolute or relative change. This was because producers could not distinguish between such changes, leading to price variations. Criticisms of this Lucas surprise model include the significant difficulty in determining whether price levels have an absolute variation. Moreover, the assumption that political shocks alone can affect production seems exaggerated. Ball et al. (1988) argue that the standard deviation of inflation, which is crucial in the output-inflation trade-off, lacks empirical support. Finally, the Keynesian Phillips Curve models integrate rational expectations into a model in which adjustment costs produce nominal rigidity, which makes current inflation dependent on expected inflation. One criticism of this model is that the producers are forced to provide the quantity demanded at a fixed contract price. Therefore, companies are always concerned with real prices. A future decrease in their prices will make the additional generated demand less profitable when the contractually agreed upon nominal price is satisfied. Empirically, Keynesian Phillips Curve models also have assumptions that do not make sense. According to Rudd (2022), standard tests of the new Phillips Curve have so many problems that they do not provide sufficient arguments to prove that expectations truly matter. Firms’ behavioral patterns show that they rarely increase their prices in anticipation. Most firms raise prices only when their costs are affected. In addition, a perfect competitive structure in which everyone competes against each other seems somewhat unlikely, as worker and customer competition have a strong local or industry-specific influence. Rudd (2022) argues that the models presented show that short-term expected inflation is the only argument in which expectations matter. Most arguments are based on limited evidence and completely disagree with the available empirical results. One important observation that supports the argument that expected inflation is not crucial is worker behavior. According to Rudd (2022), in analyzing the post-1990 economic scenario, to claim that labor suppliers ignore increases in the cost of living when accepting work for lower real wages, believing that inflation will return to the long-term average, would D. Alencar, W. Pereira, A. Lima, L. Caldas 6 be incorrect. In the context of wage negotiations, employers tend to pay wages that match the cost of living for labor-supplier agents in exchange for their continued employment. Otherwise, a significant number of layoffs would force business owners to increase the wages of the remaining workers. Similarly, when inflation remains low, employees' concerns about the cost of living decrease. However, as Rudd (2022) argues, ‘this is a story about outcomes, not expectations’ (p. 37). This theory asserts that labor suppliers expect inflation to return to its long-term average; however, in reality, workers simply do not consider recent wage increases to lag behind future changes in the cost of living. The current state of inflation dynamics shows that people do not leave their jobs because wages are not keeping pace with the cost of living, as inflation does not affect workers or wages. For Rudd (2022), the concept of adaptive expectations is irrelevant because no evidence indicates that workers negotiate higher nominal wages to anticipate inflation. Rudd (2022) argues that when policymakers use inflation expectations to determine long-term inflation, they can generate excessive concerns regarding which path inflation will follow or whether it will return to a regime with high inflation persistence. 3. Monetary Policy in Brazil from 2005 to 2022 Monetary policy plays a crucial role in a country’s economic stability and is a primary tool governments employ to control various financial factors. In Brazil, this responsibility falls upon the Central Bank, which seeks economic balance through regulating the money supply and determining interest rates. To maintain stability and promote economic development, the government utilizes monetary policy to adjust the money supply according to market conditions. During growth periods, measures may be adopted to prevent economic overheating, such as raising interest rates to discourage excessive consumption and investment. Conversely, in recessions, the government may seek to stimulate economic activity by lowering interest rates and increasing the money supply. The Central Bank is tasked with defining monetary policy and bases its decisions on a detailed analysis of economic data. To achieve the primary goal of inflation control, the National Monetary Council normalizes monetary policy, while the Central Bank's Monetary Policy Committee (COPOM) controls interest rates. Through COPOM, the government and Central Bank establish goals to control inflation and implement expansionary or contractionary policies as needed, depending on the behavior of the Brazilian economy (Ribeiro et al., 2023). Monetary policy in Brazil has undergone various transformations throughout its history. This study analyzes the evolution of monetary policy in Brazil from 2004 to 2020, highlighting key moments and the main changes over time. In a scenario marked by skepticism, Luiz Inácio Lula da Silva won the presidency in the 2002 elections. Upon Lula beginning his first term in 2003, the government faced imminent challenges, including the urgent need to reduce inflation, which had reached approximately 12.5% in the previous year owing to significant devaluation in 2002. Additionally, a pressing need existed to reduce the total net public debt, representing approximately 52% of the Gross Domestic Product (GDP), and increase international reserves, which totaled US$ 37.8 billion in 2002, including the US$ 20.8 billion borrowed from the International Monetary Fund (IMF) (Da Silva, 2017). Given the adverse conditions during the early months of the Lula administration, measures were implemented to reverse the situation. In February 2003, in response to the unfavorable environment, the Central Bank raised the Special System for Settlement and Custody (SELIC) interest rate and, consequently, the real interest rate, aiming to curb currency devaluation and its potential inflationary effects. D. Alencar, W. Pereira, A. Lima, L. Caldas 7 Government authorities deemed this action essential because of rising inflation, which exceeded 12%, surpassing the established target of 6.5%. Moreover, uncertainty regarding national economic policy demanded measures that reaffirmed the country’s commitment to orthodox policies, such as price stability and fiscal responsibility (Barbosa and Souza 2010, cited in Da Silva 2017). However, the interest rate increase proved insufficient to align inflation with the government's target. Inflation did not begin to decline until 2004, with an average appreciation of 4.95% in the exchange rate. Seizing this opportunity, the Central Bank initiated a gradual reduction in both the SELIC and real interest rates, reaching rates of 16.00% and 4.58%, respectively, in July. These decreases boosted consumption, resulting in significant economic growth, reaching a rate of 5.7%, while inflation averaged 0.4% below the upper limit of the target (Da Silva 2017). This rapid economic recovery raised concerns among monetary authorities, who feared that inflation would increase. In response, the Central Bank again raised the SELIC and real interest rates in September 2004, to 16.25% and 11.59%, respectively. These measures were implemented to contain the expectation of rising inflation and ensure economic stability (Da Silva 2017), and these decisions had noticeable effects on exchange rates and GDP growth in 2005. The gradual increase in interest rates, with the average real interest rate reaching 12.72%, contributed to a significant appreciation in the exchange rate, averaging 16.77%. This appreciation maintained inflation at 5.7%, which was within the target range. However, this resulted in a slowdown in export and investment growth, consequently affecting the GDP, which ended the year with a growth rate of 3.2%. The strong appreciation of the exchange rate did not have significant effects on net exports and, therefore, on aggregate demand because of the low GDP growth, limiting the increase in imports (Da Silva 2017). From 2003 to 2006, the economic dynamics in Brazil were characterized by the need to converge the inflation trajectory. In the first year of the Lula administration, inflation exceeded the target, driven by the ‘Lula effect,’ a term used to reflect the concern that the new administration might abandon the inflation-targeting monetary policy regime. In response to these inflationary pressures, the authorities raised interest rates and increased the fiscal surplus. From 2006 onwards, inflation began to converge towards the established target, reaching 3.14% (the target varied between 2.5% and 4.5%), compared to in 2003, 2004, and 2005, when it reached 9.3% (target 4–2.5%), 7.6% (5.5–2.5%), and 5.7% (4.5–2.5%), respectively. These measures contributed to stabilizing the inflation trajectory and promoting consistency with established targets (Ribeiro 2017). Consequently, the decrease in inflation during 2006 and 2007 was the result of not only currency appreciation but also the declines in the prices of agricultural products, indirect taxes on certain foods, and Contribution of Intervention in the Economic Domain (CIDE) on certain types of fuels. Consequently, the basic real interest rate could be reduced. At the end of 2007, the SELIC rate was 11.25%, and the real interest rate was 1.25% (average of 7.25%; Da Silva 2017). In Lula’s second term, the government faced the effects of the 2008 financial crisis by adopting Keynesian policies, aiming to overcome the negative effects on the country given the impact on the global economy. During this period, economic policy was noticeably relaxed, with measures implemented to expand consumer and borrower credit. The government adopted direct income transfer programs, granted real increases in the minimum wage, launched the Growth Acceleration Program (PAC), and expanded the role of the National Bank for Economic and Social Development (BNDES) to stimulate investment in the public and private sectors. Additionally, countercyclical measures were implemented beginning in 2009 to combat the effects of the global financial crisis (Teixeira and Pinto 2012). During his term, the government had more leeway within the inflation-targeting system, allowing for a slightly more expansionary monetary policy than in the first term. Although D. Alencar, W. Pereira, A. Lima, L. Caldas 8 inflation increased, it remained at around 4.5%, which was within the range around the target set by COPOM. Compliance with inflation targets allowed the Central Bank to adopt a more flexible approach to monetary policy. Meeting the inflation targets resulted in high interest rates, although these decreased considerably in the second term. According to economic orthodoxy, inflation control requires the use of a basic interest rate in an inflation-targeting regime (Da Silva 2017). Thus, during Lula's second term (2007–2010), the economic landscape was marked by two significant events: the impact of Chinese demand on national commodities and the 2008 financial crisis. Throughout most of this period, inflation remained within the range established by the inflation-targeting regime, with only a 5.8% inflation rate in 2010 exceeding the target of 4.5%, with a tolerance range of 2% (Ribeiro 2017). After the countercyclical measures adopted in 2009 facilitated the rapid recovery of the Brazilian economy, the Central Bank initiated a new cycle of interest rate hikes starting in April 2010, when inflation began to rise. The main reasons for this movement were related to the rapid growth of commodities imported and exported by Brazil. Although the SELIC rate experienced some fluctuations, it showed an upward trend during this period, increasing from 8.5% in April 2010 to 12.5% in July 2011. A priority at the beginning of the Dilma administration was to contain this upward movement of inflation, which reached 6.5% in March 2011, matching the upper limit of the established target (Da Silva, 2017). During Dilma Rousseff's first term, economic scenarios were heavily influenced by the intensified international financial crisis. After the initial phase of contractionary policies, the government selected a counter-crisis approach, focusing on reducing interest rates and promoting credit expansion for investments (Ribeiro 2017). Similar to the Lula administration, the Dilma administration (2011–2014) faced a recurring dilemma in the Brazilian economy: reconciling inflation targets without exceeding the ceiling and while boosting economic growth. From this perspective, a gradualist strategy was adopted, with interest rate increases and macroprudential measures implemented. Upon realizing that these measures affected growth more than inflation, the government began to reduce interest rates systematically. However, inflation did not allow the sustained decline in interest rates to last long. In late 2014, faced with stagnant economic growth, the government returned to a gradualist policy, raising interest rates and adjusting reserve requirements to stimulate credit and, consequently, aggregate demand. Thus, it resumed an approach similar to the monetary policy of the previous government, characterized by high interest rates with credit expansion (Da Silva 2017). In December 2014, at the end of Dilma Rousseff's first term, annual inflation reached 6.41%, with housing expenses being the most affected. At the end of 2014, the annual SELIC rate was 11.75%. Despite the monetary policies adopted during Lula's administration managing to please both bondholders and industrial sector entrepreneurs, Dilma Rousseff did not succeed in striking this balance and leaned more towards the interests of industrial entrepreneurs through an economic approach known as the New Economic Matrix or the Fiesp Agenda. Although the government outlined strategies that aimed to increase the GDP and reduce inflation, this attempt was unsuccessful. Under intense pressure, the impeachment process began in Dilma Rousseff's second term, which was grounded in allegations of ‘fiscal maneuvers’ and was ultimately approved by the Senate in 2016 (Viana 2022). During Michel Temer's administration, inflation control emerged as a priority, and a monetary policy was implemented that allowed the population's purchasing power to recover. Temer's administration prioritized inflation control and adopted various measures, including the release of funds from the Severance Pay Guarantee Fund (FGTS). These actions were implemented to stimulate national economic recovery. D. Alencar, W. Pereira, A. Lima, L. Caldas 15 Table A3: Heteroskedasticity Test ARCH. F-statistic 1.667299 Obs*R-squared 8.247285 Prob. F(1,49) 0.1438 Prob. Chi-Square(2) 0.1431 Adj. 𝑅 0.03 Durbin-Watson stat 2.07 Period 2004-2022 Table A4: Multiple breakpoint tests Sequential F-statistic determined breaks: 1 Break Test F-statistic Scaled Critical F-statistic Value** 0 vs. 1 * 4.276651 25.65991 20.08 1 vs. 2 1.554433 9.326596 22.11 Break dates: Sequential Repartition 1 2020M05 2020M05 Bai-Perron tests of L+1 vs. L sequentially determined breaks; Sample: 2004 2020; Break test options: Trimming 0.15, Max. breaks 5, Sig. level 0.05; Test statistics employ HAC covariances (Bartlett kernel, Newey-West fixed bandwidth) assuming common data distribution; * Significant at the 0.05 level; ** Bai-Perron (Econometric Journal, 2003) critical values. D. Alencar, W. Pereira, A. Lima, L. Caldas 16 Table A5:Autocorrelation test Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 -0.00... -0.00... 0.0192 0.890 2 0.012 0.012 0.0527 0.974 3 0.024 0.024 0.1808 0.981 4 -0.13... -0.13... 4.1929 0.381 5 -0.00... -0.01... 4.2073 0.520 6 0.008 0.011 4.2213 0.647 7 -0.06... -0.05... 5.0686 0.652 8 0.054 0.036 5.7349 0.677 9 -0.05... -0.05... 6.4337 0.696 1... -0.00... -0.00... 6.4430 0.777 1... -0.01... -0.02... 6.4788 0.840 1... -0.11... -0.10... 9.5936 0.652 1... -0.02... -0.03... 9.7332 0.716 1... 0.034 0.031 10.005 0.762 1... 0.046 0.054 10.510 0.786 1... -0.03... -0.07... 10.827 0.820 1... 0.035 0.025 11.109 0.851 1... 0.055 0.062 11.816 0.857 1... 0.023 0.029 11.946 0.888 2... 0.090 0.081 13.876 0.837 2... -0.03... -0.03... 14.088 0.866 2... -0.03... -0.02... 14.398 0.887 2... -0.01... -0.02... 14.450 0.913 2... -0.12... -0.10... 18.128 0.797 2... 0.026 0.013 18.297 0.830 2... -0.04... -0.04... 18.783 0.845 2... 0.012 0.038 18.817 0.877 2... -0.03... -0.08... 19.056 0.896 2... 0.086 0.107 20.901 0.863 3... -0.04... -0.04... 21.450 0.873 3... -0.01... -0.01... 21.531 0.897 3... -0.01... -0.00... 21.565 0.919 3... -0.07... -0.08... 22.974 0.904 3... -0.00... -0.01... 22.985 0.924 3... 0.008 -0.03... 23.002 0.940 3... -0.10... -0.11... 25.765 0.897 D. Alencar, W. Pereira, A. Lima, L. Caldas 17 Table A6: VAR Lag Order Selection Criteria Lag LogL LR FPE AIC SC HQ 0 -4654.908 NA 1.17e+12 44.81643 44.91270 44.85535 1 -2897.479 3396.570 75895.50 28.26422 28.93815* 28.53672* 2 -2848.193 92.41172 66848.66 28.13647 29.38805 28.64254 3 -2808.878 71.44644 64886.98 28.10460 29.93383 28.84425 4 -2772.902 63.30542 65157.77 28.10482 30.51170 29.07804 5 -2737.362 60.48510 65868.27 28.10925 31.09378 29.31604 6 -2707.177 49.63086 70323.28 28.16517 31.72735 29.60553 7 -2657.949 78.10333* 62754.25* 28.03797* 32.17780 29.71190 8 -2630.368 42.16722 69269.88 28.11892 32.83640 30.02643 * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion Table A7: Cointegration Test Data Trend: None None Linear Linear Quadratic Test Type No Intercept Intercept Intercept Intercept Intercept No Trend No Trend No Trend Trend Trend Trace 3 3 3 3 3 Max-Eig 3 3 3 3 2 Note: Selected (0.05 level*) Number of Cointegrating Relations by Model. *Critical values based on MacKinnon-Haug-Michelis (1999).