Área 3 - Macroeconomia, Economia Monetária e Finanças

Term Spread and Macroeconomy in Brazil

Joaquim Pinto de Andrade Universidade de Brasíliajandrade@unb.br 61 93808337

Manoel Carlos de Castro PiresIPEAmanoel.pires@ipea.gov.br61 93808337

Luiz Alberto D´Ávila de AraújoBanco do Brasil S.A.davila@bb.com.br61 93808337

Resumo: Este artigo investiga a existência de não-linearidades na curva de juros brasileira, identificar as principais variáveis macroeconômicas podem explicar o spread do termo e mudanças na política econômica. A conclusão mostra a importância da taxa de inflação atual para explicar o spread da curva de juros brasileira. Além disso, encontramos que o risco Brasil, medido pelo EMBI + Brasil, é a variável relevante para explicar as mudanças no regime de política monetária. Adicionalmente, observa-se que a taxa de inflação é positiva e significativa para explicar as mudanças na estrutura a termo de juros e o resultado primário é relevante para entender os períodos de instabilidade na economia.

Código JEL: E31, E43, E52Palavras-chave: inflação, estrutura a termo de juros, política monetária.

Abstract: This article investigates the existence of nonlinearities in Brazilian yield curve, identify the main macroeconomic variables can explain the term spread and change in economic policy. The conclusion shows the importance of the current inflation rate to explain the spread of interest rates for interbank short term. Furthermore, we find that the Brazil risk, measured by the EMBI + Brazil, is the relevant variable to explain changes in monetary policy regime. Inflation rate is positive and significant to explain changes in yield curve. In addition to that the fiscal surplus is relevant during periods of instability in the economy.

JEL codes: E31, E43, E52Keywords: inflation, yield curve, monetary policy.

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Term Spread and Macroeconomy in Brazil

1 Introduction

Nowadays, central banks seek to conduct monetary policy by establishing effective communication among the participants of the financial market, to reduce the uncertainty of its action on short term interest rates and provide market information to assess the expected path long-term interest rates. In other words, the monetary authority uses short-term interest rate as an instrument of monetary policy to affect the long-term interest of the economy, which is the rate that matters to change the aggregate demand.

It is important to answer how changes in expectations of monetary policy and fiscal policy can modify the long-term rates and also check whether the observed long-term movements are in disagreement with the actions of the monetary authority in the short run. Note that long-term interest rates can embed a risk premium associated with the maturity of the securities, but if the term structure follow the hypothesis of rational expectations this premium is null or constant in time and long-term rates are an average of short-term rates. However, some studies indicate that the spread of the term is not constant and, therefore, the expectations hypothesis is no longer valid, for example, Mankiw and Miron (1986), Andrade and Tabak (2001) and Issler and Lima (2003). If this occurs, it becomes necessary to identify the variables responsible for the premium to improve the predictability of the macroeconomic variables.

The empirical evidence cited in the previous paragraph indicates that the failure of the expectations hypothesis may be due to the non-linearity of the term structure of the interest rate. To solve this problem we have "threshold" models, which are a good option to identify the variables that may be responsible for changes in the slope, curvature and spread of the yield curve. Aditionnaly, we find in the literature, that the change in yield curve over the business cycle may be associated with recessions, as Dombrosky and Haubrich (1995), Stock and Watson (2001) and Hamilton and Kim (2002). Accordingly, the yield curve may provide information to anticipate recessions (slope from positive to negative) because the award of long-term bonds have countercyclical behavior (investors do not want to take risks in uncertain times), and pro-cyclical yields on short run (monetary policy reduces the short-term yields during the recession to stimulate economic activity). Note that the presence of the inflation rate may enhance the positive slope of the curve, since the money tomorrow will have a smaller value than today, while a deflation could have the opposite effect.

Regarding the Brazilian data, we must note two important facts. The first fact shows that it is common to observe an "almost" inversion of the term structure, ie, times when abrupt increases in the short term interest rates are not always accompanied by increases in long-term rate. The second fact relates to the assymetric rate of change in the spread between short and long where is common to observe abrupt elevations, while falls are slower.

This section concludes that the spread of maturity has a nonlinear behavior measured by the regression model smooth transition - STR and that this nonlinearity depends on the macroeconomic policy regime adopted. Following this introduction; section 2 provides a literature review of the relationship between macroeconomics and the term structure of interest rates; section 3 discusses the expectations hypothesis and the non-linearity; section 4 presents the model used in this investigation; section 5 formalizes the econometric estimation and discusses the empirical results for the Brazilian case and; section 6 contains the conclusion of the discussions raised.

2 Macroeconomic Variables and Term Structure of Interest Rates

The study of the term structure of interest rates and its relationship with macroeconomic variables has increased in recent years. The new line of research attempts to identify the macroeconomic forces that affect the movements of the structure of interest rates, indicating how the monetary authority is influencing market expectations about the present and future trajectory of interest.

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Bernanke (1983) used the spread of credit risk calculated as the difference between the rate of commercial paper and Treasury bills rate of the U.S. as a predictive instrument of production in the United States.

Stock and Watson (1989) explained the economic cycle through the credit spread (the difference between government bonds and commercial paper) and the term spread (difference between the rates of long-and short-term government securities), the latter being representative of bond yield curve (or term structure of interest rates).

The importance of the credit spread comes from the fact that it represents the credit risk (risk of default or late payment) which is an indication to anticipate the recession process (with the credit channel). On the other hand, the importance of the term spread is linked to information from the monetary stance, with the belief in the ability of the agents to conduct monetary policy in the economic environment to be pursued.

In the analysis of the credit spread or spread short, Bernanke (1990) showed that a restrictive monetary policy by increasing the rates of fedfunds has the effect of increasing the cost of funds for banks. To avoid this increase in cost of funding, banks must choose between issuing certificates of deposit (CD in the U.S. or in Brazil CBD), to reduce its loan portfolio, sell government securities from its portfolio of assets and/or increase the rate interest charged on loans. The first two actions increase the rate of commercial paper in relation to government bonds (CDs and commercial paper are substitutes). The increase of loans leads firms to choose to borrow in commercial paper, which increases the difference between commercial paper and government bonds. The option to sell government securities from its own portfolio has an opposite impact, ie, reduces the spread between the rate of commercial papers and the rate of government bonds, it increases the rate of government bonds. However, as banks not sell government bonds easily, because they represent a highly liquid asset that can protect against liquidity risk, or risk of lacking the resources to honor its contractual commitments to maturity or the risk of unexpected withdrawals of deposits.

In the analysis of the spread of the term, Campbell (1995) defined the fixed-income securities, as papers that pay a specified value to investors. Therefore, to evaluate a bond it is not necessary to quantify the random future payments (such as shares), you only need to discount the future payments and bring these flows to present value. It should be noted that some bonds are not in accordance with this conception, because issuers can delay payments. However, in the public securities it is possible to disregard that risk of default.

To understand the term structure of interest rates, Campbell used a numerical example to explain the formation of expectations in the bond market. Think of a 30-year bond whose return (or yield) is 7% per year and other evidence of one year whose return is 4% per year. At first, it seems that the return of 7% is better than the return of 4%, but we must consider that the return of 4% yield is a right within one year, while 7% will be certain only after 30 years. Assuming the one year is reinvested annually in the next 29 years, then the return of 4% after the first year, would yield the same as the of 29 years if the other pay 7.1%. At this point there is the theory of expectations hypothesis, whose premise is to match a strategic long-term investment (or 30 years) with the investment strategy that involves thirty short-term applications of one year.

Note that the bond market indicates that the interest rate is contracted to a future date through a spot rate of interest. Thus, if we consider a spot rate of 10% and 11% for investments of one and two years, then the future rate of 1 year should be in place in the second year would be 12%. Thus, an application of 11% for two years would yield the same application in one year yielding a 10% and in another two years yielding 12%.

Therefore, the hypothesis of rational expectations applied to the term structure of interest rates defines the term premium as the expected difference between the yield to retain a long-term basis and the return of an emergency short term. This award represents the additional income to retain a long-term asset, rather than applying in a short term asset. When the slope of the term strutcture is positive there is good evidence that the long term rate will increase and in the opposite case - slope be negative - is indicative of the rate of long term must fall.

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When considering only the importance of bringing all future payments to present value, disregarding the credit risk, it is possible to realize the importance of the term structure of interest rates, since it represents the rates used to make this temporal change in the value of cash flows. Another relevant aspect is that although we do not consider the credit risk, fluctuations in the term structure of interest rates cause an oscillation in the present value of cash flows and affect the expected return (and thus the interest rate) of the holders of financial assets.

Thus we see that the term structure has an impact on key economic variables, while we know that the monetary authority seeks to form market expectations regarding the future path of interest rates. In this article we are only interested in evaluating the impact of central bank activity in the formation of expectations about future rates, in other words, the impact of macroeconomic variables on the term structure of interest rates.

To clarify the inclusion of macroeconomic variables we follow Diebold, Rudebusch and Aruoba (2006) that provided a way to introduce financial macroeconomic variables in the specification of the term structure of interest rates.

3 Expectations hipothesis and Econometric model to nonlinearities

The theory of expectations is one of the more traditional theories, their origin is due to Fischer (1896) and indicates that an investor to carry a bond for a long time appropriates an income that is an average of fluctuating rates of those who speculated in that period. The argument is based on the idea of arbitration, because with arbitrage opportunities makers have incentives to borrow in the short term and lend long-term (short-term rate lower than the long-term rate).

As the expectations hypothesis establishes a relationship between the long-term rates and short-term rates, the spread (or risk premium due) can be considered as the slope of the term structure.

Given some inconclusive results of the present value models used to test the approach of expectations, it is common to use enlarged models that incorporate other variables, not just interest rates. Evans for example, studies the effect of fiscal policy, particularly of deficits on interest rates. Evans (1985) finds evidence that "large" deficits affect the interest rate of long term and not short term, changing thus the term structure. Evans (1987) shows that there are temporary effects associated with announcements of deficits on the short-term interest rate.

In the applications of term structure to Brazilian data, we find this expanded model. For example, Rocha, Moreira Magalhaes (2002) analyze the importance of foreign debt in sovereign bond spreads. In the same vein, Matsumura and Moreira (2005) study the importance of macroeconomic variables in the determination of spreads.

In the case of the term structure of bonds in the domestic market, a source of research is to study, like Evans, the effect of fiscal policy on the term structure. This is one of the main conclusions obtained by Issler and Lima (2003, p.896):

"There is an open field of research to test alternative theories about the term structure in Brazil, and ... examine the role of public debt management can be one of the paths to tread."

Even as “augmented” term structure models establish themselves as important sources of research, the relevance of non-linearity should not be underestimated. The time series of spread presented in Lima and Issler (2003) shows that it is common to see abrupt shocks followed by gradual reductions in the spread.

This stylized fact can be studied from the nonlinear time series, using for example models of "threshold". In that model, the dependent variable is a function of the independent variables in a peculiar way: the dependent variable is described by a linear process to a certain limit (or "threshold"), from which the relationship of the variables changes.

In this case, the critical aspect of the model is to identify the region where there is a change in the dynamic model, ie, to identify the and, moreover, how many regions are there.

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The approach "threshold" is based on Hansen (2000), which provided the possibility of dividing the sample and using an indicator function with observable variables to determine the split of the sample into subgroups. This regression model can be described as:

(1)(2)

The variable "threshold" is defined by and is used to divide the sample into groups that can be considered as classes or arrangements of economic policy. The random variable corresponds to the regression error.

Linear x Nonlinear Model (LSTR1 ou LSTR2)

In Diebold et ali (2006), are parameters, is the slope factor defined as "long term yield less short term yield" ( or "slope"), is the level ( or "level") and represents the curvature ( or "curvature"), where the dynamic of follows a first order autoregressive process:

(3)

With, , and , in matrix notation:(4)

(5)Diebold et ali (2006) relate to macroeconomic variables, making the extension of the

model that did not present macroeconomic variables to a type system like: . This new system defines a model of the term structure of interest rates

with macroeconomic variables of capacity utilization ( ), short-term interest rate ( ) and inflation rate ( ).

Supose an observed a sample , where and are real values, and is a vector of dimension m. The variable "threshold" may be an element of and is assumed as having a continuous distribution.

Defining a dummy variable where is the indicator function and doing , the model equations are summarized:

(6)Where denotes the effect "threshold."As Teräsvirta (2007), the nonlinear models have gained importance in macroeconomics and

financial modeling and can be divided into two broad categories. The first category includes models that do not have the linear model as a special case. The second includes several popular models that have the linear model. In this paper, the discussion is a model for economic time series regression models with smooth transition (Smooth Transition Regression - STR).

The STR model is a model of non-linear regression and can be seen as a development of the model of regression switching.

The standard STR model is defined as:  (7)

Where , is a vector of explanatory variables , and a vector of exogenous variables . Thus , and are vectors of parameters and .

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The transition function has a limit and is a continuous function in space for any parameter value , is the slope parameter and is a vector of location parameters, where

.The last term of equation (7) indicates that the model can be interpreted as a linear model with

stochastic coefficients that vary in time . The transition function is a logistic function of the general type:

 (8)

Where is a restriction of identification, the equations (7) and (8) together define the function Logistics STR (LSTR).

When then the transition function and the STR model is a linear model. In this case the choice for K is restricted to or . For , the parameters change monotonically as a function of from up to . For , they change symmetrically around the midpoint , where the logistic function reaches its minimum value. The minimum value is between zero and, reaching zero when and where . The parameter controls the slope and provide the location of the transition function.

The model LSTR with (LSTR2) is appropriate in situations where local behavior of the process is similar for both large and small values of and different in the middle. When the model LSTR2 shows the result of the regression model with three switching regimes, where the arrangements are identical, and the outer system is different from the medium.

The STR model parameters are estimated using the conditional maximum likelihood. The log-likelihood is maximized numerically with Numerical derivatives for this purpose. Finding good initial values for the algorithm is important. Thus, when from the transition equation are fixed, STR is linear in the parameters.This suggests constructing a grid, estimate the remaining parameters conditional to or for , and calculate the sum of the square of the residuals. The process is repeated for N combinations of these parameters, picking the values of the parameters that minimize the sum of the square of the residuals.

4 Empirical analysis in Brazilian Economy

This section uses a database with monthly information for the period August 1997 to September 2011 (169 observations). The historical series of Future Pre x DI were obtained from the BM&F for the construction of the term structure of the interest rates, the primary result was obtained by the concept "below the line" with information from the Central Bank of Brazil and the values are reported as percentage of GDP data for the last twelve months (SUP), the rate of inflation measured by the National Index of Consumer Prices for 12 months was obtained from the IBGE (IPCA) and the Selic rate was obtained from the Central Bank of Brazil (SELIC), the rate the dollar/real was obtained by PTAX800 from the Central Bank of Brazil (DOLLAR). 

The evolution of the EMBI+Brazil (Emerging Markets Bond Index) was obtained from Bloomberg to create a series of Brazil Risk and allows us to assess the risk of dependence on international capital along the Brazilian economy to international investors (RBrazil). Additionally, the explanatory variables lagged were included for model specification.

Table 1 - Sample Descriptive Statistics - 1997/08 to 2011/09

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Variable Mean Median Min Max Std-Dev CV Asymmetry KurtosisRbrazil 580 461 142 2395 418 1.388 1.528 3.097SELIC 16.077 16.578 7.132 40.014 5.917 2.717 1.393 2.710IPCA 6.303 2.142 1.645 17.236 2.973 2.120 1.800 4.090SUP 1.901 102.940 -0.253 3.059 0.810 2.345 -1.151 0.445Spread_3 months 0.110 0.030 -1.865 5.989 0.617 0.178 6.116 54.740Spread_6 months 0.142 0.060 -3.761 8.370 0.966 0.147 4.384 37.364Spread_1 year 0.185 0.108 -5.473 8.330 1.223 0.151 1.928 17.201Spread_2 years 0.251 0.331 -6.537 7.517 1.425 0.176 0.632 8.528Spread_5 years 0.506 0.499 -7.608 5.489 1.938 0.261 0.047 2.631Spread_10 years 0.739 0.594 -7.590 6.820 2.306 0.321 0.331 1.659

Source: Statistics compiled by the authors.

Table 1 shows the descriptive statistics from the sample used for empirical investigation of the Brazilian economy. This table shows a positive slope of the term structure of interest because it suggests a behavior where the average spread for maturities of 3 and 6 months and 1, 2, 5 and 10 years ranges from 0.11% to 0.73%. Note that the minimum and maximum rates amounted to -7.61% and +8.37% per year, are checked in the spread measured by the difference between the rate of 10 years and the rate of one day. The standard deviation of the sample indicates significant variance in the sample, that grows for longer terms. The variable SUP provides an average result of 1.90% of capacity utilization of the Brazilian economy. The IPCA and the Brazil Risk, present also significant dispersion in the data, ranging from 1.64% to 17.24% per year and 142 to 2395 basis points, respectively.

Figure 1 shows that the long-term rates were well above the rates of short-term for the periods: 07/1999 to 09/1999, 06/2001 to 03/2003, 06/2004 to 10/2004, 05/2008 to 09/2008 and 11/2009 to 06/2010, while for the rest of the sample, there were no significant differences.

Figure 1 - IPCA, ETTJ and the Term Spread

-6.00-4.00-2.000.002.004.006.008.00

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Spread3m Spread6m Spread1y

Spread2y Spread5y Spread10y

On the other hand, Figure 1 also shows that the term structure of interest rates in Brazil has not always present a positive slope, indicative of prosperity and economic growth (spread with values above zero). A relevant aspect to be observed indicates that, in principle, there is an inverse relationship between inflation rate and the spread. Additionally, the period from 2002 to 2003 shows evidence of a non-linear movement in the variables analyzed.

The non-linearity is an important aspect to be analysed, being indicative of changes in economic regimes arising from financial crises (or other shocks) that must be identified - start of the period and end, as well as explain how during these crises macroeconomic variables affect the behavior of interest rates in financial markets, signaling a greater or lesser strength of monetary and fiscal policies.

The finding of the relationship between inflation rate and Selic rate policy is reinforced by Figure 2, where there are indications that the IPCA inflation has had a role in setting the basic interest rate of the economy, for a good part of data.

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Figure 2 - Selic versus IPCA (least squares adjustment)

To provide additional insight on why the spread decreases when inflation increases (or increases, when inflation decreases), Figure 3 shows the effect of real interest rates over the term of one year.

Figure 3 - Real Interest Rate vs Interest Rate Expected Inflation vs. Long-Term Focus

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IPCA RealInterest ETTJ1y

Source: term structure of expected inflation was constructed by the authors based on information disclosed in the Focus survey, obtained from the Central Bank of Brazil.

The analyzes of Figures 1 and 3 provide subsidies that the negative relationship between inflation rate and a spread of maturity, is possibly associated with a reduction in real interest rate of the Brazilian economy.

Figure 4 - Brazil Risk, Exchange Rate and Primary Balance / GDP

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0.000.501.001.502.002.503.003.504.00

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-0.500.000.501.001.502.002.503.003.50

SUP

Source: Brazil Risk obtained from Bloomberg (EMBI +), Exchange Rate and the primary surplus by the term "below the line" obtained from the Central Bank of Brazil.

Another macroeconomic variable relevant to the Brazilian economy is the exchange rate real/dollar and Brazil risk.  As shown in Figure 4, the period 2002/2003 showed high growth of the Brazil risk premium, the period in which the rates of long-term interest of the term structure of interest rates and the risk premium term (see Figure 1) showed significant elevation.

To assess the impact of fiscal policy on the level of interest rates in the Brazilian economy, the primary surplus, measured by the term "below the line" the Central Bank of Brazil (SUP), show an increasing surplus in relation to Gross Domestic Product - GDP (in the last twelve months) by the end of 2008, as Figure 4. However, from 2009 the surplus began to decrease and then increased again from 2010 on.

The latest macroeconomic variable followed in this analysis represents the level of real economic activity in relation to the potential level, measured by the difference between the Level of Physical Industrial Production (II) and the series that result from the application of the Hodrick-Prescott – HP filter (HP_II), as Figure 5. Note that industrial production was affected by the financial crisis (subprime crisis started in August 2007).

Figure 5 - Physical Industrial Production, and Potential Output Gap

80.0000

85.0000

90.0000

95.0000

100.0000

105.0000

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120.0000

II HP_II

Source: Table 2295, concerning the physical industrial production index by type and sections and industrial activities, obtained from the IBGE. Potential product obtained through the application of HP filter in the series of physical production.

Thus, it is clear that the Brazilian economy presents some characteristics that may indicate non-linearity, whose consequences may be altering the behavior of the term structure of interest rates and the spread of the term. In addition, sharp increases and slow decreases underscore the need for adoption of non-linear instrumental, contemplating some macroeconomic variables and analyzing their outcomes, contained in the literature of monetary and fiscal policy.

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Term Spread and Macroeconomic Variables in Brazil

This section sets out the econometric model to estimate and evaluate the empirical aspects of macroeconomics, the term structure of interest rates and the spread of maturity observed in Brazil.

Diebold, Rudebusch and Aruoba (2006) suggested that the incorporation of macroeconomic variables in the estimation of the term structure of interest rates is important to explain the factors of political economic that are affecting the fluctuations of interest rates in the economy. Thus, this paper aims to assess the impact of macroeconomic variables on the spread of the term structure of interest rates in Brazil, obtained in the financial market.

This section investigates empirically in Brazil, if there is a relationship between the spread of maturity and some macroeconomic variables that reflect the conduct of economic policy of a country. The macroeconomic variables chosen represent the primary surplus of the economy, foreign trade, the global risk aversion in relation to Brazil and the inflation rate. In turn, the effects of the term structure of interest rates are considered as the rate recorded in operations in the futures market PRE x DI, and for the first point of the curve (1 day) is used the CDI and for the others are used the rates for future ID contracts (buying and selling future), obtained at various times from the file-BM&F Bovespa.

Other macroeconomic variables were tested but were not significant in this non-linear modeling, among which we highlight the exchange rate and the expectation of future inflation (Central Bank Focus survey).

The consumer price index was obtained from the IBGE and calculated with monthly figures recorded in the last twelve months. The primary surplus concept "below the line" as a percentage of GDP over the last twelve months. The proxy for dependence on international capital is the level of country risk measured by EMBI + Brazil, the higher the price implies a higher perception of risk by international financial market on the perspectives of the Brazilian economy.

Therefore, the aim of this paper is to explain the behavior of the term spread through the impacts from macroeconomic variables, combining the effects of economic policy with the movements in financial markets, providing subsidies for economic policy makers, in particular, the formulator of monetary policy.

Initially, to understand the behavior of the term structure of interest rates is necessary to estimate the spread of the term, starting from the forward rate equation:

 (9)After finding the series of the maturing spread, the goal is to explain it in terms of the no

observable economic variables that represent monetary policy, the balance of public accounts, foreign trade and the slope/curvature of interest rates in Brazil:

 (10)Where SPR is the spread calculated as the difference between the rate of long-term interest rate

and one day DI. The long-term interest rate is obtained in the market of futures Pre x DI traded at BM&F and the rate of short-term interest rate is the one day DI found in the financial market.

IPCA is the rate of inflation defined by the Consumer Price Index Broad, SUP is the primary surplus measured by the term "below the line" of the Central Bank of Brazil, Dollar is the exchange rate calculated by the real-dollar PTAX800 and RBrazil is the country risk measured by the EMBI+Brazil and the last term is the prediction error of the spread. The subscript t represents the month of realization of the data, and superscripts n, m are the term referring to the risk premium spread between the long-term rate m and the short-term n verified in the financial market.

The spread of maturity may have nonlinear behavior and, therefore, it is adopted the STR model to identify the change of regimes and to estimate the regression for each of the samples with different characteristics.

 However, for applying the "threshold" model is necessary to define the transition variable that would explain the change between regimes. To choose the transition variable several variables were tested like inflation rate, the primary surplus, capacity utilization, level of physical production, the Brazil

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risk and the output gap. The choice of the model followed the Akaike information criteria (AIC), Schwarz (SC) and Hannah-Quinn (HQ).

Equation (10) was estimated by Smooth Transition Regression model - STR, as Teräsvirta (2007). The choice of this econometric estimator focused on the suspicion of the presence of non-linearity in the variables of the sample. In particular, the suspicion was reinforced by the historical behavior of the term structure of interest rates, the spread of the term, the risk of inflation and Brazil.

Some results are expected in the estimation. The variable level of consumer prices (IPCA) has resulted in an expected positive effect on interest rates term structure.

The primary outcome (SUP) has the expected result a negative effect on the spread of the term structure of interest rates. This result is expected because the Central Bank of Brazil discloses the primary concept "below the line" to represent the amount of resources obtained by the government which will be deducted from the net public sector debt. Therefore, the higher the primary surplus, the lower the national debt, is implying a lower perception of risk, indicative of lower spread of the term interest rates.

The exchange rate (Dollar) results in an expected negative effect on the spread of the term structure of interest rates. This result is expected because by raising the exchange rate real/dollar is expected to increase in interest rates, the increase being greater in shorter terms. Therefore, the rate with short term increasing more than long-term reduces the spread.

Another control variable reflects global risk aversion in relation to the Brazilian economy (RBrazil) measured by the EMBI+Brazil, whose intended effect is positive, that is, the higher the country risk the greater the spread of the term demanded by foreign investors and domestic because the pricing of country risk is measured by the weighted average of Brazilian securities traded abroad relative to the bonds of the same feature of the U.S. government. Note that this effect stems from the fact that the securities included in the determination of country risk are long term and pricing to market these bonds already embeds an expected future path for the two economies and in particular Brazil.

Table 2 - Testing Linearity against STR

Termo F F4 F3 F2 Modelo3 months 3.80E-07 3.96E-03 5.47E+00 1.05E+01 LSTR16 months 2.31E-11 4.41E-04 2.96E-01 5.75E-02 LSTR1

1 year 1.17E-10 7.72E-04 3.92E-01 1.40E-01 LSTR12 years 1.58E-08 7.44E-03 1.08E+00 9.39E-01 LSTR15 years 3.16E-04 1.44E+00 1.85E+01 1.02E+01 LSTR1

10 years 2.94E-03 1.73E+01 2.43E+01 6.26E+00 LSTR1Sample: [1997 M9 2011 M9] T = 169

p-values of F-tests - transition variable RBrazil(t):

After the indication of the expected impacts on the control variables in estimating the spread of the term, the next step is to estimate equation (14) and apply econometric tests of model specification. The first step is to test for the existence or non-linearity in the model. The choice of the value of K ( or ) indicated the use of logistic regression model soft LSTR1, as can be seen in Table 2.

It should be noted, though, that have been evaluated in several lags spread the word and the macroeconomic variables, but the model was reduced with the elimination of redundant variables, leaving only the Spread, IPCA, Surplus, Dollar and, RBrazil with a lag in time.

Then, we made several estimates of equation (10), one for each of the spreads of the terms relating the term structure of interest rates, which are: 3 months, 6 months, 1 year, 2 years, 5 years and 10 years. Turning this estimation with the explanatory variables mentioned above, the Akaike information criterion (AIC) was used to choose the model among the candidate models, as the favorite one that minimized the AIC value. To assess the quality of the model specification, the tests were not applied Godfrey autocorrelation test and homoscedasticity called ARCH-LM, assessing whether the waste does not reject the null hypothesis and reached the results in Table 3.

Table 3 - Tests of Model Specification

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lag / p-value 3 months 6 months 1 year 2 years 5 years 10 years1 0.2353 0.1283 0.1122 0.2335 0.0749 0.02812 0.5288 0.3084 0.0793 0.0338 0.0948 0.04863 0.0462 0.0280 0.0119 0.0092 0.0932 0.04058 0.0690 0.0995 0.0678 0.0600 0.2822 0.1195

3 months 6 months 1 year 2 years 5 years 10 yearsp-value (c2) 0.4959 0.0504 0.0033 0.0007 0.0580 0.1672p-value (F) 0.4636 0.0351 0.0014 0.0002 0.0412 0.1378

Test of No Error Autocorrelation

ARCH-LM Test

The estimation of the spread of term structure of interest rates supports the conclusion that Diebold, Rudebusch and Aruoba (2004) and it appears that macroeconomic variables have some explanatory power on the volatility of the term spread of interest rates observed Brazilian financial market.

One of the main variables adopted the inflation targeting regime in force in Brazil during the sample period is the level of prices in the economy measured by the IPCA. In this context, the monetary authority determines the basic Selic rate in response to shocks and to achieve the stabilization of the economy. The coefficient is positive IPCA on the linear part of the estimation, showing that the effect of short-term rate, or 1 day, is less than the effect on the rate of long term. It is noteworthy that the largest positive effect (greater impact on long-term rate) in terms of 6 months, 1 year, 2 years and 5 years. Importantly, the coefficients had the expected statistical significance, except the term of 10 years where the p-value was 0.13 in - but close to the 0.10 expected. In the non-linear estimation, we observe that the coefficients have the opposite effect and all estimated coefficients were significant, indicating that the effect of inflation occurs to a greater extent in the short-term rates, this is indicative of negative relationship between inflation and the spread salary for investment in driving economic conditions.

Table 4 – STR Model – Brazilian Economyestimate p-value estimate p-value estimate p-value estimate p-value estimate p-value estimate p-value

Linear PartConstant -0.3925 0.2947 -0.7370 0.0678 -0.9613 0.0343 -0.9936 0.0475 -0.2323 0.6981 0.1239 0.8470Spread(t-1) -0.3190 0.0000 -0.2125 0.0026 -0.0681 0.3419 0.0536 0.4675 0.2847 0.0002 0.3850 0.0000Ipca(t) 0.3765 0.0479 0.4924 0.0154 0.6223 0.0063 0.7063 0.0051 0.5362 0.0851 0.4956 0.1365Sup(t) -0.1384 0.7590 0.0306 0.9498 0.1588 0.7723 0.2505 0.6804 0.5366 0.4519 0.6191 0.4161RBrazil(t) 0.0021 0.1744 0.0046 0.0053 0.0069 0.0002 0.0084 0.0000 0.0099 0.0001 0.0103 0.0001Dolar(t) -1.5016 0.2134 -1.8759 0.1482 -1.8704 0.2005 -1.6193 0.3158 -1.4107 0.4637 -1.0442 0.6100Ipca(t-1) -0.3752 0.0386 -0.4817 0.0130 -0.6011 0.0058 -0.6816 0.0047 -0.5616 0.0575 -0.5428 0.0865Sup(t-1) -0.0014 0.9976 -0.0937 0.8496 -0.1727 0.7570 -0.2469 0.6895 -0.4698 0.5169 -0.6066 0.4335RBrazil(t-1) -0.0023 0.1082 -0.0047 0.0022 -0.0070 0.0001 -0.0084 0.0000 -0.0092 0.0001 -0.0094 0.0002Dollar(t-1) 1.8255 0.1186 2.2594 0.0728 2.2906 0.1065 2.0335 0.1944 1.4610 0.4311 1.0222 0.6041Nonlinear PartConstant 9.2638 0.0000 11.3392 0.0000 10.9398 0.0003 9.7904 0.0030 4.8774 0.1724 3.5311 0.3840Spread(t-1) 0.5850 0.0004 0.4512 0.0029 0.3101 0.0623 0.1762 0.3614 -0.2584 0.2498 -0.4031 0.1069Ipca(t) -3.2045 0.0017 -4.3511 0.0012 -5.1269 0.0023 -5.2853 0.0056 -5.5618 0.0000 -5.9455 0.0000Sup(t) -26.7692 0.0087 -32.9896 0.0222 -38.9276 0.0304 -39.3966 0.0440 -40.3836 0.0002 -43.3575 0.0004RBrazil(t) -0.0205 0.0000 -0.0284 0.0000 -0.0325 0.0000 -0.0326 0.0000 -0.0313 0.0000 -0.0309 0.0000Dolar(t) 27.9603 0.0000 35.9496 0.0001 39.5148 0.0009 37.9613 0.0038 35.7477 0.0000 35.4680 0.0000Ipca(t-1) 1.5779 0.0823 2.2362 0.0579 2.6745 0.0763 2.6970 0.1179 3.2105 0.0056 3.3827 0.0060Sup(t-1) 4.9465 0.2531 5.0061 0.3341 6.1623 0.3031 6.4718 0.3186 4.7349 0.3502 6.5796 0.2392RBrazil(t-1) -0.0046 0.0966 -0.0042 0.2069 -0.0041 0.3066 -0.0037 0.4019 -0.0053 0.1347 -0.0071 0.0636Dollar(t-1) -0.6854 0.8025 -0.4788 0.8803 2.0015 0.5870 4.3873 0.2763 9.9400 0.0103 13.0576 0.0029Gamma 14.48 0.1087 15.75 0.0794 19.72 0.1780 23.52 0.3319 3819.32 0.9967 1080.18 0.8351C1 1204.01 0.0000 1213.10 0.0000 1220.02 0.0000 1219.65 0.0000 1164.96 0.0000 1164.91 0.0000

Transition function LSTR1 LSTR1 LSTR1 LSTR1 LSTR1 LSTR1AIC 0.2428 0.3936 0.6402 0.8449 1.1619 1.2847SC 0.6519 0.8027 1.0493 1.2540 1.5710 1.6938HQ 0.4088 0.5596 0.8062 1.0109 1.3279 1.4507Adjusted R2 0.4742 0.5403 0.5171 0.4885 0.5121 0.5729Variance of residual 1.1289 1.3127 1.6797 2.0614 2.8301 3.1999SD of residuals 1.0625 1.1457 1.2960 1.4357 1.6823 1.7888Estimated Model: Spread = Constant + Spread(t-1) + Ipca + Surplus + Dollar + RBrazil + Ipca(t-1) + Surplus(t-1) + Dollar(t-1) + RBrazil(t-1)Transition variable: RBrazil(t)

5 yearsVariables 10 years3 month 6 months 1 year 2 years

12

In the linear part, the primary outcome (SUP) did not show the expected negative impact on the level variable, only the lagged variable, but both variables did not show statistical significance. In the non-linear, the negative effect was observed with significant coefficients, indicating that during times of turbulence control of the primary surplus is important to explain the term structure of interest rates, to generate credibility that the amount of resources obtained by the government have the beneficial impact of reducing the net public sector debt. Therefore, the higher the primary surplus, the lower the national debt, is implying a lower perception of risk, indicating less spread of the term interest rates.

The estimated coefficients for the exchange rate (Dollar) were not statistically significant in the linear part. The same happened in the non linear part.

The transition variable, which represents the global risk aversion in relation to the current Brazilian economy, Rbrazil, presented the expected positive effect, indicating that greater reliance on international capital implies higher premium term risk of interest rates in the Brazilian financial market. In the non-linear positive relationship of this variable was significant but presented a negative relationship. Although RBrazil be essential to identify the nonlinearity of the series analyzed (periods of shocks in the Brazilian economy), the magnitude of the coefficients obtained in both the linear and nonlinear part, was very low and shows that this variable is not relevant to explain variations in the risk premium term interest rates in Brazil.

Therefore, even in a partial equilibrium model that considers only the direction of macroeconomic variables influencing the spread of interest, the incorporation of macroeconomic variables is relevant to explain the spread of the term interest rates and, consequently, the slope of the term structure Brazilian interest rates.

5 Conclusions

The objective of this study was to explain the movements of the slope of the term structure of interest rates as a function of observable macroeconomic variables. We also use an econometric non-linear estimator to find the variable slope and curvature of the Brazilian interest rates.

The findings indicate that monetary policy has a significant effect on the differential between interest rates of short and long term. In particular, it was found that the coefficient is positive IPCA on the linear part of the estimation, showing that the effect of short-term rate is higher than the effect on the rate of long term. Thus, by controlling inflation through monetary policy, the Central Bank is managing the expectations of financial markets and short term interest rates. The primary surplus is relevant in times of economic instability (the non-linear estimation) because the negative effect with significant coefficients suggests that the primary surplus is important to generate credibility that the amount of resources obtained by the government will be sufficient to control net debt and thereby lower the risk perception of the financial market, evidenced by the reduction of the term spread of interest rates.

Additionally, one of the most relevant results of this research is to find that a macroeconomic variable can explain changes in the term structure of interest rates in the Brazilian economy (slope and curvature), in particular, stands out its relevance to explain the moments of crisis . In the Brazilian economy, and the sample, the variable that performs this function is the Brazil risk, measured by the EMBI + Brazil.

Thus, it was possible to observe the relevance of the partial equilibrium model to evaluate the effect of macroeconomic variables in a single direction (macroeconomic variables influencing the spread of interest), to explain the slope of the term structure of interest rates in Brazil.

References13

[1] Bernanke, B. S. (1983). "Nonmonetary Aspects of the financial crisis in the propagation of the great depression", The American Economic Review, vol. 73, p. 257-276.[2] ________ (1990). "On the predective power of interest rates and interest rate spreads," New England Economic Review, Federal Reserve Bank of Boston, p. 51-68.[3] Campbell, J. Y. (1995). "Some lessons from the yield curve," Journal of Economic Perspectives, vol. 9, no. 3, p. 129-152.[4] Diebold, Francis X. & Rudebusch, Glenn D. & Boragan Aruoba, S. (2006). "The macroeconomy and the yield curve: a dynamic latent factor approach", Journal of Econometrics, Elsevier, vol.  131 (1-2), pages 309-338.[5] Evans, P. (1985). Do Large Deficits Produce High Interest Rates? The American Economic Review, 75 (1), 68-87.[6] ________ (1987). Interest Rates and Expected Future Budget Deficits in the United States. The Journal of Political Economy, 95 (1), 34-58.[7] Fisher, I. (1896). Appreciation and interest. Publications of the American Economic Association, 11, 21-29.[8] Hamilton, James D. and H. Dong Kim (2002). A Re-Examination of the Predictability of the Yield Spread for Real Economic Activity. Journal of Money, Credit, and Banking, 34, 340-60.[9] Hansen, B. E. (2000). Sample splitting and "threshold" estimation. Econometrica, vol. 68, no. 3, 575-603.[10] Haubrich, Joseph G. and Ann M. Dombrosky (1996). Predicting Real Growth Using the Yield Curve, Federal Reserve Bank of Cleveland Economic Review, vol. 32, no. 1 (one quarter 1996) p. 26-35.[11] Lee, A. M. C. and J.V. Issler (2003). The Expectations Hypothesis of the Term Structure of Interest in Brazil: An Application of Present Value Models. Journal of Economa, 57 (4): 873-898.[12] Mankiw, N. Gregory and Jeffrey A. Miron (1986). The Changing Behaviour of the Term Structure of Interest Rates. The Quarterly Journal of Economics, vol. 101, No. 2, p. 211-228.[13] Matsumura, M. and A. Moreira (2005). Macroeconomics Variávels Can Account for the Structure of Sovereign Spreads? Studying the Brazilian Case. IPEA Discussion Paper No. 1106.[14] Rock, K., Moreira, A. and R Magalhães (2002). Determinants of Brazilian Spread: A Structural Approach. IPEA Discussion Paper No. 890.[15] Stock, James H. and Mark W. Watson (1989). New Indexes of Coincident and Leading Economic Indicators, in Olivier Blanchard and Stanley Fischer, NBER Macroeconomics Annual, Cambridge MA: MIT Press.[16] ________ (2001). "Forecasting Output and Inflation: The Role of Asset Prices," NBER Working Papers 8180, National Bureau of Economic Research.[17] Tabak, B. and S. Andrade (2001). Testing the expectations hypothesis in the Brazilian term structure of interest rates. Brasília: Central Bank of Brazil Working Paper nr. 30.[18] Teräsvirta, Timo (2007). Smooth Transition Regression Modeling. Themes in modern econometrics: Applied Time Series Econometrics, ch. 6, 222-242, Cambridge University Press. 

14

Appendix I - Evolution of yield curve and term premium of the Brazilian financial market

Inversions in the Term Structure of Interest Rates Brazilian Financial Market

18.00

20.00

22.00

24.00

26.00

28.00

ETTJ_29

ETTJ_91

ETTJ_183

ETTJ_366

ETTJ_731

ETTJ_1830

03/2003 04/2003 05/200306/2003 07/2003 08/2003

14.00

15.00

16.00

17.00

18.00

19.00

20.00

ETTJ_29

ETTJ_91

ETTJ_183

ETTJ_366

ETTJ_731

ETTJ_1830

09/2004 11/2004 01/200502/2005 04/2005 05/2005

8.00

10.00

12.00

14.00

16.00

18.00

ETTJ_2

9

ETTJ_9

1

ETTJ_1

83

ETTJ_3

66

ETTJ_7

31

ETTJ_1

830

01/2006 03/2006 04/2006 08/200604/2007 05/2007 08/2007 12/2007

Data Crescimento do PIB1998 0.04%1999 0.25%2000 4.31%2001 1.31%2002 2.66%2003 1.15%2004 5.71%2005 3.16%2006 3.97%2007 6.08%2008 5.14%2009 -0.19%   

Spread of the Term Interest Rate of the Brazilian Financial Market

-4.00

-2.00

0.00

2.00

4.00

6.00

RiscoD

I_29

RiscoD

I_91

RiscoD

I_18

3

RiscoD

I_36

6

RiscoD

I_73

1

RiscoD

I_18

30

12/1999 01/2000 02/2000 03/200004/2000 05/2000 06/2000 07/200008/2000 09/2000 10/2000 11/2000

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

RiscoD

I_29

RiscoD

I_91

RiscoD

I_18

3

RiscoD

I_36

6

RiscoD

I_73

1

RiscoD

I_18

30

05/2002 06/2002 07/2002 08/2002 09/200210/2002 11/2002 12/2002 01/2003 02/200303/2003 04/2003 05/2003 06/2003 07/2003

-4.00

-2.00

0.00

2.00

4.00

RiscoD

I_29

RiscoD

I_91

RiscoD

I_18

3

RiscoD

I_36

6

RiscoD

I_73

1

RiscoD

I_18

30

01/2004 02/2004 03/2004 04/200405/2004 06/2004 07/2004 08/200409/2004 10/2004 11/2004 12/2004

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

01/200

6

03/200

6

05/200

6

07/200

6

10/200

6

12/200

6

02/200

7

04/200

7

06/200

7

08/200

7

10/200

7

12/200

7

RiscoDI_29 RiscoDI_91 RiscoDI_183RiscoDI_366 RiscoDI_731 RiscoDI_1830

15

Appendix II - Brazilian Yield Curve

The vertices that make up the term structure of interest rates in the Brazilian financial market forms a curve of interest rates denominated fixed rate curve without boxes.

This curve is calculated daily and shows the interest rates for future periods (vertices or terms) in a funded compound, on an annual basis with 252 working days.

The vertices chosen to form the Brazilian yield curve are: 1 day, 1 month, 3 months, 6 months, 1 year, 2 years, 5 years and 10 years.The first term, one day, using the CDI rate that reflects the market Interfeinanceiro Deposit. While the other vertices using futures contracts DI x Pre traded at BM & F – Bovespa.

The attainment of the vertices is greater than one day using the equation below:

Where: = Yield curve called preset without cash for the period in days t, with a funded and made

to 252 days. = PU adjustment of BM & F - Bovespa for the futures contract traded for DI x Pre t days.

t = corresponds to the term working days of the futures contract DI x Pre.Some additional aspects need to be clarified to understand how it was formed the yield

curve. Initially, note that when the maturity of the futures contract falls úteil one day ahead, was considered the daily rate of CDI.

When the desired vertex (1 month, 3 months, etc.) fall between the expiration of two futures contracts, will be the interpolation rate built in this period through the following equation:

Where: = The annual interest rate obtained through interpolation between the two interest rates

obtained for two different maturities of futures contracts on BMF & BOVESPA.= Time in days to be interpolated.

= Factor for the cumulative period .

= Factor for the cumulative period .

 = Time in days regarding the expiration of previous contract.

 = Term referring to the days of contract expiration posterior.

Note that the accumulated factor for term t days corresponds to 2521

tj ETTJF , and to ETTJ on

weekdays is expressed by compound capitalization and considering 252 working days.When there is a holiday in Sao Paulo, home of BMF & BOVESPA, the update will be made of

the rates of the previous day CDI rate of one working day, ie.After otenção rates for each of the terms (1 day, 1month, 3 months, 6 months, 1 year, 2 years, 5

years and 10 years) and each day in the sample, it is necessary to determine the rate the terms for the months that make up the sample and that will be used to make pet on a monthly basis.

Obtaining the terms of the monthly fee is made by bringing the annual rate to 252 days to one working day and accumulated for each of the rates of each day that makes up the month and then the monthly fee is annualized as follows:

16

Thus, we obtain a sample with rates that make up the term structure of interest rates for each month that makes up the sample on which to be

17