Download 2 Macroeconomic Variables and Term Structure of Interest

Área 3 - Macroeconomia, Economia Monetária e Finanças
Term Spread and Macroeconomy in Brazil
Joaquim Pinto de Andrade
Universidade de Brasília
[email protected]
61 93808337
Manoel Carlos de Castro Pires
IPEA
[email protected]
61 93808337
Luiz Alberto D´Ávila de Araújo
Banco do Brasil S.A.
[email protected]
61 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, E52
Palavras-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, E52
Keywords: inflation, yield curve, monetary policy.
1
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.
2
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.
3
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 shortterm 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 x and, moreover, how many x regions are there.
4
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:
yi  1/ xi  ei ,
qi  
(1)
yi   2/ xi  ei ,
qi  
(2)
The variable "threshold" is defined by qi and is used to divide the sample into groups that can
be considered as classes or arrangements of economic policy. The random variable ei corresponds to the
regression error.
Linear x Nonlinear Model (LSTR1 ou LSTR2)
In Diebold et ali (2006), 1 ,  2 ,  3 and  are parameters,  2 is the slope factor defined as "long
term yield less short term yield" ( S t or "slope"), 1 is the level ( Lt or "level") and  3 represents the
curvature ( C t or "curvature"), where the dynamic of Lt , S t and Ct follows a first order autoregressive
process:
 Lt   L   a11 a12 a13  Lt 1   L   t L  

 

 

(3)
 S t   S    a 21 a 22 a 23  S t 1   S    t S  
C     a

 

C 
 t
 31 a32 a33  Ct 1   C   t C 
With, f t  Lt St Ct  ,    L
 f t     A f t 1     t
/
S
C / and t  1,, T , in matrix notation:
(4)
(5)
yt  f t   t
model

f t  Lt
Diebold et ali (2006) relate Lˆt , Sˆt , Cˆ t to macroeconomic variables, making the extension of the
that did not present macroeconomic variables to a type system like:
St
Ct
UCt
itm
 t  . This new system defines a model of the term structure of interest
/
rates with macroeconomic variables of capacity utilization ( UCt ), short-term interest rate ( itm ) and
inflation rate (  t ).
Supose an observed a sample
yi , xi , qi nj1 , where
yi and qi are real values, and xi is a
vector of dimension m. The variable "threshold" qi may be an element of xi and is assumed as having a
continuous distribution.
Defining a dummy variable d i    I qi    where I 
 is the indicator function and doing
xi    xi d i   , the model equations are summarized:
yi   2/ xi   n/ xi    ei
(6)
Where  n   2  1 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)
yt   / zt   / zt G , c, st   ut    G , c, st  zt  ut
5
Where t  1,, T , z t  wt/ , xt/  is a vector of explanatory variables wt/  1, yt 1 ,, yt  p  , and a
/
vector of exogenous variables xt  x1t ,, xkt  . Thus t  0 ,1 ,, m , , and    0 ,1 ,, m , are
/
/
/
m  1 1 and u t ~ iid 0,  2 .
The transition function G , c, st  has a limit s t and is a continuous function in space for any
/
parameter value s t ,  is the slope parameter and c  c1 ,, ck  is a vector of location parameters, where
vectors of parameters
c1    ck .
The last term of equation (7) indicates that the model can be interpreted as a linear model with
stochastic coefficients that vary in time   G , c, st  . The transition function is a logistic function of
the general type:
1
K




(8)
G , c, st   1  exp    st  ck   ,   0
k

1




Where   0 is a restriction of identification, the equations (7) and (8) together define the
function Logistics STR (LSTR).
When   0 then the transition function G , c, st   1 / 2 and the STR model is a linear model.
In this case the choice for K is restricted to K  1 or K  2 . For K  1 , the parameters   G , c, st 
change monotonically as a function of s t from  up to    . For K  2 , they change symmetrically
around the midpoint c1  c2  / 2 , where the logistic function reaches its minimum value. The minimum
value is between zero and, reaching zero when    and where c1  c2 and    . The parameter 
controls the slope and c1 and c2 provide the location of the transition function.
The model LSTR with K  2 (LSTR2) is appropriate in situations where local behavior of the
process is similar for both large and small values of s t 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 loglikelihood is maximized numerically with Numerical derivatives for this purpose. Finding good initial
values for the algorithm is important. Thus, when  and c from the transition equation are fixed, STR is
linear in the parameters.This suggests constructing a grid, estimate the remaining parameters  and 
conditional to  ,c1  or  , c1 , c2  for K  2 , 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
6
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
Variable
Rbrazil
SELIC
IPCA
SUP
Spread_3 months
Spread_6 months
Spread_1 year
Mean
580
16.077
6.303
1.901
0.110
0.142
0.185
Median
461
16.578
2.142
102.940
0.030
0.060
0.108
Min
142
7.132
1.645
-0.253
-1.865
-3.761
-5.473
Max
2395
40.014
17.236
3.059
5.989
8.370
8.330
Std-Dev
418
5.917
2.973
0.810
0.617
0.966
1.223
CV
1.388
2.717
2.120
2.345
0.178
0.147
0.151
Asymmetry
1.528
1.393
1.800
-1.151
6.116
4.384
1.928
Kurtosis
3.097
2.710
4.090
0.445
54.740
37.364
17.201
Spread_2 years
Spread_5 years
Spread_10 years
0.251
0.506
0.739
0.331
0.499
0.594
-6.537
-7.608
-7.590
7.517
5.489
6.820
1.425
1.938
2.306
0.176
0.261
0.321
0.632
0.047
0.331
8.528
2.631
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
Spread3m
Spread6m
Spread1y
Spread2y
Spread5y
Spread10y
12/2010
02/2010
04/2009
06/2008
08/2007
10/2006
12/2005
02/2005
04/2004
06/2003
08/2002
10/2001
12/2000
02/2000
04/1999
06/1998
08/1997
8.00
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
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,
7
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.
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
40.00
32.00
24.00
16.00
8.00
IPCA
RealInterest
12/31/2010
2/28/2010
4/30/2009
6/30/2008
8/31/2007
10/31/2006
12/31/2005
2/28/2005
4/30/2004
6/30/2003
8/31/2002
10/31/2001
12/31/2000
2/29/2000
4/29/1999
6/29/1998
8/29/1997
0.00
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.
8
Figure 4 - Brazil Risk, Exchange Rate and Primary Balance / GDP
3,000
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
2,500
2,000
1,500
1,000
500
0
RBRAZIL
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
-0.50
DOLLAR
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
120.0000
115.0000
110.0000
105.0000
100.0000
95.0000
90.0000
85.0000
80.0000
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 nonlinearity, 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.
9
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:
SPRtn ,m  itn  it1  Lt  RBrazil t  SUPt  Dollart   t   t
(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:
SPRtn ,m  c1  c 2 Ipca t  c3 SUPt  c 4 Dollart  c5 RBrazil t  t
(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
10
tested like inflation rate, the primary surplus, capacity utilization, level of physical production, the Brazil
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
p-values of F-tests - transition variable RBrazil(t):
Termo
F
F4
F3
F2
3 months
3.80E-07
3.96E-03
5.47E+00 1.05E+01
6 months
2.31E-11
4.41E-04
2.96E-01
5.75E-02
1 year
1.17E-10
7.72E-04
3.92E-01
1.40E-01
2 years
1.58E-08
7.44E-03
1.08E+00
9.39E-01
5 years
3.16E-04
1.44E+00 1.85E+01 1.02E+01
10 years
2.94E-03
1.73E+01 2.43E+01 6.26E+00
Sample: [1997 M9 2011 M9] T = 169
Modelo
LSTR1
LSTR1
LSTR1
LSTR1
LSTR1
LSTR1
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 ( K  1 or K  2 ) 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.
11
Table 3 - Tests of Model Specification
lag / p-value
1
2
3
8
3 months
0.2353
0.5288
0.0462
0.0690
3 months
p-value (c2)
p-value (F)
0.4959
0.4636
Test of No Error Autocorrelation
6 months
1 year
2 years
0.1283
0.1122
0.2335
0.3084
0.0793
0.0338
0.0280
0.0119
0.0092
0.0995
0.0678
0.0600
ARCH-LM Test
6 months
1 year
0.0504
0.0351
0.0033
0.0014
5 years
0.0749
0.0948
0.0932
0.2822
10 years
0.0281
0.0486
0.0405
0.1195
2 years
5 years
10 years
0.0007
0.0002
0.0580
0.0412
0.1672
0.1378
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 Economy
Variables
Linear Part
Constant
Spread(t-1)
Ipca(t)
Sup(t)
RBrazil(t)
Dolar(t)
Ipca(t-1)
Sup(t-1)
RBrazil(t-1)
Dollar(t-1)
Nonlinear Part
Constant
Spread(t-1)
Ipca(t)
Sup(t)
RBrazil(t)
Dolar(t)
Ipca(t-1)
Sup(t-1)
RBrazil(t-1)
Dollar(t-1)
Gamma
C1
3 month
estimate p-value
6 months
estimate p-value
1 year
estimate p-value
2 years
estimate p-value
5 years
estimate p-value
10 years
estimate p-value
-0.3925
-0.3190
0.3765
-0.1384
0.0021
-1.5016
0.2947
0.0000
0.0479
0.7590
0.1744
0.2134
-0.7370
-0.2125
0.4924
0.0306
0.0046
-1.8759
0.0678
0.0026
0.0154
0.9498
0.0053
0.1482
-0.9613
-0.0681
0.6223
0.1588
0.0069
-1.8704
0.0343
0.3419
0.0063
0.7723
0.0002
0.2005
-0.9936
0.0536
0.7063
0.2505
0.0084
-1.6193
0.0475
0.4675
0.0051
0.6804
0.0000
0.3158
-0.2323
0.2847
0.5362
0.5366
0.0099
-1.4107
0.6981
0.0002
0.0851
0.4519
0.0001
0.4637
0.1239
0.3850
0.4956
0.6191
0.0103
-1.0442
0.8470
0.0000
0.1365
0.4161
0.0001
0.6100
-0.3752
-0.0014
-0.0023
1.8255
0.0386
0.9976
0.1082
0.1186
-0.4817
-0.0937
-0.0047
2.2594
0.0130
0.8496
0.0022
0.0728
-0.6011
-0.1727
-0.0070
2.2906
0.0058
0.7570
0.0001
0.1065
-0.6816
-0.2469
-0.0084
2.0335
0.0047
0.6895
0.0000
0.1944
-0.5616
-0.4698
-0.0092
1.4610
0.0575
0.5169
0.0001
0.4311
-0.5428
-0.6066
-0.0094
1.0222
0.0865
0.4335
0.0002
0.6041
9.2638
0.5850
-3.2045
-26.7692
-0.0205
27.9603
1.5779
4.9465
-0.0046
-0.6854
14.48
1204.01
0.0000
0.0004
0.0017
0.0087
0.0000
0.0000
0.0823
0.2531
0.0966
0.8025
0.1087
0.0000
11.3392
0.4512
-4.3511
-32.9896
-0.0284
35.9496
2.2362
5.0061
-0.0042
-0.4788
15.75
1213.10
0.0000
0.0029
0.0012
0.0222
0.0000
0.0001
0.0579
0.3341
0.2069
0.8803
0.0794
0.0000
10.9398
0.3101
-5.1269
-38.9276
-0.0325
39.5148
2.6745
6.1623
-0.0041
2.0015
19.72
1220.02
0.0003
0.0623
0.0023
0.0304
0.0000
0.0009
0.0763
0.3031
0.3066
0.5870
0.1780
0.0000
9.7904
0.1762
-5.2853
-39.3966
-0.0326
37.9613
2.6970
6.4718
-0.0037
4.3873
23.52
1219.65
0.0030
0.3614
0.0056
0.0440
0.0000
0.0038
0.1179
0.3186
0.4019
0.2763
0.3319
0.0000
4.8774
-0.2584
-5.5618
-40.3836
-0.0313
35.7477
3.2105
4.7349
-0.0053
9.9400
3819.32
1164.96
0.1724
0.2498
0.0000
0.0002
0.0000
0.0000
0.0056
0.3502
0.1347
0.0103
0.9967
0.0000
3.5311
-0.4031
-5.9455
-43.3575
-0.0309
35.4680
3.3827
6.5796
-0.0071
13.0576
1080.18
1164.91
0.3840
0.1069
0.0000
0.0004
0.0000
0.0000
0.0060
0.2392
0.0636
0.0029
0.8351
0.0000
Transition function
LSTR1
LSTR1
AIC
0.2428
0.3936
SC
0.6519
0.8027
HQ
0.4088
0.5596
Adjusted R2
0.4742
0.5403
Variance of residual
1.1289
1.3127
SD of residuals
1.0625
1.1457
Estimated Model: Spread = Constant + Spread(t-1) + Ipca + Surplus
Transition variable: RBrazil(t)
LSTR1
LSTR1
LSTR1
LSTR1
0.6402
0.8449
1.1619
1.2847
1.0493
1.2540
1.5710
1.6938
0.8062
1.0109
1.3279
1.4507
0.5171
0.4885
0.5121
0.5729
1.6797
2.0614
2.8301
3.1999
1.2960
1.4357
1.6823
1.7888
+ Dollar + RBrazil + Ipca(t-1) + Surplus(t-1) + Dollar(t-1) + RBrazil(t-1)
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 nonlinear 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.
13
References
[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
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[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, 575603.
[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
20.00
28.00
19.00
26.00
18.00
24.00
17.00
22.00
16.00
20.00
15.00
18.00
09/2004
02/2005
05/2003
08/2003
ETTJ_731
ETTJ_366
ETTJ_183
ETTJ_91
ETTJ_29
ETTJ_1830
ETTJ_731
04/2003
07/2003
11/2004
04/2005
01/2005
05/2005
ETTJ_1830
03/2003
06/2003
ETTJ_366
ETTJ_183
ETTJ_91
ETTJ_29
14.00
18.00
16.00
14.00
12.00
10.00
01/2006
04/2007
03/2006
05/2007
04/2006
08/2007
ETTJ_1830
ETTJ_731
ETTJ_366
ETTJ_183
ETTJ_91
ETTJ_29
8.00
08/2006
12/2007
Data
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Crescimento do PIB
0.04%
0.25%
4.31%
1.31%
2.66%
1.15%
5.71%
3.16%
3.97%
6.08%
5.14%
-0.19%
Spread of the Term Interest Rate of the Brazilian Financial Market
6.00
10.00
8.00
4.00
6.00
2.00
4.00
0.00
2.00
0.00
-2.00
-2.00
12/1999
04/2000
08/2000
01/2000
05/2000
09/2000
02/2000
06/2000
10/2000
03/2000
07/2000
11/2000
4.00
05/2002
10/2002
03/2003
06/2002
11/2002
04/2003
07/2002
12/2002
05/2003
RiscoDI_1830
RiscoDI_731
RiscoDI_366
RiscoDI_183
RiscoDI_91
RiscoDI_29
RiscoDI_1830
RiscoDI_731
RiscoDI_366
RiscoDI_183
RiscoDI_91
-4.00
RiscoDI_29
-4.00
08/2002
01/2003
06/2003
09/2002
02/2003
07/2003
2.00
1.00
2.00
0.00
0.00
-1.00
-2.00
-2.00
-3.00
01/2004
05/2004
09/2004
02/2004
06/2004
10/2004
03/2004
07/2004
11/2004
04/2004
08/2004
12/2004
RiscoDI_29
RiscoDI_366
15
RiscoDI_91
RiscoDI_731
RiscoDI_183
RiscoDI_1830
12/2007
10/2007
08/2007
06/2007
04/2007
02/2007
12/2006
10/2006
07/2006
05/2006
03/2006
-4.00
01/2006
RiscoDI_1830
RiscoDI_731
RiscoDI_366
RiscoDI_183
RiscoDI_91
RiscoDI_29
-4.00
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:
252


 100.000  t 



ETTJ t  
1
 PU t  


Where:
ETTJ t = Yield curve called preset without cash for the period in days t, with a funded and made
to 252 days.
PU t = 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:

 F
ii   F j  k
  F j

ti t j
 t k t j








252
ti
1
Where:
ii = The annual interest rate obtained through interpolation between the two interest rates
obtained for two different maturities of futures contracts on BMF & BOVESPA.
t i = Time in days to be interpolated.
Fj
t
= Factor for the cumulative period j .
Fk
= Factor for the cumulative period t k .
tj
= Time in days regarding the expiration of previous contract.
tk
= Term referring to the days of contract expiration posterior.
Note that the accumulated factor for term t days corresponds to F j  ETTJ t  252 , 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.
1
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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:
ETTJ
month
t


0
  1  ETTJ t1 businessday


1
252
252

   1  ETTJ

1
last businessday 252
t
 nr. businessday in month
1


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
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