ISSN 1518-3548

Nonlinear Mechanisms of the Exchange Rate Pass-Through:A Phillips curve model with threshold for Brazil

Arnildo da Silva Correa and André Minella

November, 2006

Working Paper Series

ISSN 1518-3548 CGC 00.038.166/0001-05

Working Paper Series

Brasília

N. 122

Nov

2006

P. 1-30

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3

Nonlinear Mechanisms of the Exchange Rate Pass-Through:

A Phillips curve model with threshold for Brazil *

Arnildo da Silva Correa** André Minella**

The Working Papers should not be reported as representing the views of the Banco Central do Brasil. The views expressed in the papers are those of the author(s) and do not necessarily

reflect those of the Banco Central do Brasil.

Abstract This paper investigates the presence of nonlinear mechanisms of pass-through from the exchange rate to inflation in Brazil. In particular, it estimates a Phillips curve with a threshold for the pass-through. The paper examines whether the short-run magnitude of the pass-through is affected by the business cycle, direction and magnitude of exchange rate changes, and exchange rate volatility. The results indicate that the short-run pass-through is higher when the economy is growing faster, when the exchange rate depreciates above some threshold and when exchange rate volatility is lower. These results have important implications for monetary policy and are possibly related to pricing-to-market behavior, menu costs of price adjustment and uncertainty about the degree of persistence in exchange rate movements. Keywords: Exchange Rate Pass-Through, Threshold, Inflation, Nonlinearity, Brazil JEL Classification: E31, E50, E58

* We are thankful to Fabio Araújo and Tomiê Sugahara for their participation in initial estimations, Carlos Hamilton Araújo, Ana Beatriz Galvão and Marcelo Kfoury Muinhos for suggestions, Érica Oliveira and Ibitisan Santos for assistance with data, and others colleagues at the Research Department of the Central Bank of Brazil for their contributions and comments. The views herein are those of the authors and do not necessarily reflect those of the Central Bank of Brazil. ** Research Department, Central Bank of Brazil. E-mails: arnildo.correa@bcb.gov.br and andre.minella@bcb.gov.br

4

1. Introduction

The presence of nonlinearities in the Phillips curve has relevant implications for

monetary policy. The slope of the Phillips curve – measuring the response of inflation to

output gap – affects directly the cost of disinflation. Schaling (2004) shows that, when the

Phillips curve is convex, that is, the sensitivity of inflation to economic activity increases

with the level of output, the optimal monetary policy reaction function is asymmetric.

Nonlinearity may also be present in the pass-through from exchange rate changes to prices.

If the pass-through, for instance, is greater when the economy is booming, we may consider

that the central bank's reaction to a depreciation of the domestic currency will be stronger in

this context.

In fact, the investigation of the presence of nonlinear mechanisms in the Phillips

curve has been an important topic in the recent literature.1 Most studies on nonlinear

Phillips curves for developed economies have focused on the slope of the Phillips curve and

the exchange rate pass-through. In the first case, Laxton, Rose and Tambakis (1999) and

Bean (2000) find evidence that the Phillips curve is convex, while Stiglitz (1997) and

Eisner (1997) claim that the Phillips curve is concave.2 The literature on exchange rate

pass-through, in turn, reports several sources of nonlinearity, indicating that the degree of

pass-through can be related to some macroeconomic variable, including the exchange rate.

Mann (1986), Goldberg (1995), Gil-Pareja (2000), Mahdavi (2002) and Olivei (2002) have

found asymmetric pass-through related to the direction of exchange rate changes, while

Ohno (1989) and Pollard and Coughlin (2004) have indicated the presence of asymmetry

associated with the magnitude of exchange rate changes.

The business cycle is also pointed out as an important source of nonlinearity for the

pass-through. The transmission of exchange rate depreciations to domestic prices would be

lower during an economic slowdown. Goldfajn and Werlang (2000), estimating a panel

data model for 71 countries, have found that depreciations have a higher pass-through to

prices when the economy is booming. In the case of Brazil, Carneiro, Monteiro and Wu

1 See, for instance, Chadha, Masson and Meredith (1992), Laxton, Meredith and Rose (1995), Dupasquier and Ricketts (1998), Nobay and Pell (2000), Aguiar and Martins (2002), Tambakis (1999), and Clements and Sensier (2003).

5

(2002) have found similar results estimating a backward-looking Phillips curve with the

pass-through coefficient as a function of unemployment rate and real exchange rate level.3

In these papers, the magnitude of the pass-through coefficient is a function of some

variables.

This paper investigates the possibility of a nonlinear pass-through in Brazil using

threshold models. These models are part of a class of models that consider different states

of nature or regimes and allow different dynamic behavior for the variables, conditional on

the regime prevailing in each moment (Franses and van Dijk, 2000). In the case of

threshold models, the sample is divided into classes based on whether the value of an

observed variable surpasses or not some threshold. This kind of model – Threshold

Autoregressive (TAR) Model – was initially proposed by Tong (1978) and Tong and Lim

(1980) and has spread in the recent applied economic literature.

We focus on the pass-through because exchange rate movements have played a key

role in the inflation dynamics in Brazil, especially in the early years of the inflation

targeting regime with recurrent bouts of exchange rate depreciation in response to shocks,

in the context of balance of payments vulnerabilities. We estimate three specifications for

the Phillips curve, which differ basically by the variable used as the threshold for the pass-

through: i) output gap; ii) nominal exchange rate change; and iii) exchange rate volatility.

Thus, we can deal with different possible sources of nonlinearity. The first question is

whether economic activity affects the magnitude of the pass-through. The second one is

whether the pass-through is symmetric with respect to the direction of the exchange rate

change – whether appreciations or depreciations have symmetric effects on prices – and to

the magnitude of the exchange rate change.

The estimations indicate that the short-run pass-through is higher when the economy

is growing faster, when the exchange rate depreciates above a threshold value and when

exchange rate volatility is lower. These results have implications for monetary policy and

are possibly related to pricing-to-market behavior, costs of changing prices, and uncertainty

regarding the degree of persistence of exchange rate changes.

2 Filardo (1998), in turn, considers that the Phillips curve is neither entirely convex nor concave, but a combination of both (a concave-convex curve). 3 Muinhos (2001) has found mixed results, and Bogdansky, Tombini and Werlang (2000) work with a model for Brazil with a nonlinear pass-through as well.

6

The article is organized as follows. Section 2 sets forth the methodology of

threshold models with the presence of endogenous variables. Section 3 presents the

specifications of the Phillips curve with threshold and the estimation results. The last

section concludes the text.

2. Threshold models with endogenous variables

In threshold models, the sample is divided into classes based on the value of an

observed variable – whether it surpasses or not some threshold. As usual in practice, the

threshold is not known and needs to be estimated. The simplest model is the SETAR (Self-

Exciting Threshold Autoregressive Model), where the threshold is given by a lagged term

of the dependent variable – yt-d, where d>0. An AR(1) model of two regimes and d=1 can

be written as:

⎩⎨⎧

≥++⟨++

=−−

−−

τεφφτεφφ

112

120

1111

10

ttt

tttt yify

yifyy , (1)

where � is the threshold value, jiφ are the parameters i of the regime j, and tε is an i.i.d.

white noise sequence conditional on the history of the series, denoted by

},,...,{ 111 ptpttt yyy −−−−− =Ω , with zero mean and variance 2σ . Alternatively, this model can

be expressed as:

tttttt yIyyIyy ετφφτφφ +≥++⟨−+= −−−− )()()](1)[( 112

12011

11

10 , (2)

where I(.) is an indicator function that takes a value equal to either one or zero, depending

on the regime at time t.

For these models with exogenous regressors, there is a well-developed theory of

inference and estimation4. In the case of models with endogenous variables, in turn, the

theory is still working in progress. Caner and Hansen (2004) develop an estimator and an

4 See, for example, Chan (1993), Hansen (1996, 1999, 2000) and Caner (2002).

7

inference theory for this kind of model, with the restriction that the threshold variable must

be exogenous.

A model with endogenous regressors can be described as follows. Let ntttt xzy 1},,{ =

be the information set, where ty is unidimensional, tz is an m-dimension vector

(regressors), and tx is a k-dimension vector (instruments), with k��� ��� �������

variable )( tt xqq = can be an element or a function of the vector xt. In a general way, the

structural equation can be written as:

⎩⎨⎧

≥+=⟨+=τζθτζθ

tttt

tttt

qzyqzy

'2

'1 , (3)

or in a more compact way,

tttttt qIzqIzy ζτθτθ +≥+⟨−= )()](1[ '2

'1 , (4)

where 'jθ are parameter vectors, Τ∈τ , and T is the set of the possible threshold values.

Since the error term tζ is correlated with tz – at least one variable in vector tz is

endogenous – equation (4) cannot be estimated by ordinary least squares (OLS) because

parameters would be biased and inconsistent.

The method proposed by Caner and Hansen (2004) is based on the estimation of a

reduced form equation for the endogenous variables as a function of instrumental variables,

that is, a model with the conditional mean of the endogenous variables as a function of

exogenous variables. The estimated values are plugged into structural equation (4) and the

threshold value is estimated by minimizing the sum of the squared residuals. The

parameters of the structural equation are estimated in a third step, when the sample is

divided according to the estimated threshold. The estimation is conducted using the two-

stage least square method (2SLS) or the generalized method of moments (GMM).

Therefore, the first stage (conditional expectations model of tz ) is given by:

8

ttt uxfz += ),( β , (5)

0)|( =tt xuE , (6)

where β is a vector with parameters, ut is the error term, and (.,.)f is a function. In

particular, this function can also be conditioned on the threshold value (which can be equal

or different from that in the structural equation):5

)]()[()](1)[(),( '2

'1 τβτββ ≥+⟨−= ttttt qIxqIxxf . (7)

The parameter vector β in equation (5) can be obtained by OLS, for each � ∈ T,

as:

)]([)]([)(ˆ1

'1

1

'1 τττβ ⟨⎟⎟⎠

⎞⎜⎜⎝

⎛⟨= ∑∑

=

−

=t

n

ttt

n

tttt qIzxqIxx , (8)

)]([)]([)(ˆ1

'1

1

'2 τττβ ≥⎟⎟⎠

⎞⎜⎜⎝

⎛≥= ∑∑

=

−

=t

n

ttt

n

tttt qIzxqIxx . (9)

Using parameters β , we can obtain the values tz that will replace tz in the

structural equation. Doing it recursively for every � ∈ T, the threshold value in the

structural equation can be chosen by the minimization of the sum of the squared residuals,

using a grid search. For every �, let Y, ZL and ZG denote the vector yt and the matrices

)]([ τ⟨tt qIz e )]([ τ≥tt qIz , respectively. Thus, the threshold estimator is obtained from:

)(minargˆ τττ

nT

S∈

= , (10)

where )(τnS is the sum of the squared residuals in the regression of Y on LZ and GZ . The

set of threshold values in (10) should be such that each regime has sufficient observations

5 In this paper, we do not condition on the threshold value in this first stage.

9

to generate reliable parameter estimation. According to Franses and van Dijk (1999), a safe

choice is at least 15% of the sample.

Given the estimated threshold value τ , the sample is divided into subsamples, and

parameters of equation (10) can be estimated by 2SLS as:

( ) ( ) ⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡=

−−−YXXXXZZXXXXZ LLLLLLLLLLL

'1''1

'1''1

ˆˆˆˆˆˆˆˆˆˆˆθ , (11)

( ) ( ) ⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡=

−−−YXXXXZZXXXXZ GGGGGGGGGGG

'1''1

'1''2

ˆˆˆˆˆˆˆˆˆˆˆθ , (12)

where LZ , GZ , LX e GX stand for the matrices with observations )]ˆ([ τ⟨tt qIz ,

)]ˆ([ τ≥tt qIz , )]ˆ([ τ⟨tt qIx and )]ˆ([ τ≥tt qIx , respectively.

Caner and Hansen (2004) show that those estimators are consistent, although not

necessarily efficient. Their applicability is conditioned on the exogeneity of the threshold

variable.

3. Phillips curve model for Brazil

Aiming to test the possibility of the presence of a nonlinear pass-through from the

exchange rate to inflation, we estimate some Phillips curve models for Brazil combined

with the methodology of regime switching described in the previous section.

The estimated Phillips curve relates inflation to a measure of real disequilibrium

(output gap), inflation expectations, past inflation, exchange rate changes and external

inflation, with a threshold variable:

⎩⎨⎧

≥+++Δ+−−+=⟨+++Δ+−−+=

−−−−+

−−−−+

τεαπαπααπαπτεαπαπααπαπ

ttttttttLt

ttttttttLt

qifyeEqifyeE

124

*11

221

22

211

21

114

*11

121

12

111

11

)()1()()1(

, (13)

where jiα is the parameter of a specific regressor i when the economy is in regime j, L

tπ is

free IPCA inflation (headline inflation measured by the Broad National Consumer Price

10

Index, but excluding administered prices), tπ is headline IPCA inflation, *tπ is a measure

of external inflation (PPI in the U.S.), ty is output gap (actual minus potential output)6, te

is the natural logarithm of the average nominal exchange rate (domestic currency units per

dollar), Et(.) is the expectations operator conditional on the information available at t, Δ is

the difference operator ( 211 −−− −=Δ ttt eee ), tε is a residual, tq is the threshold variable,

andτ ∈T, where T is the set of possible values for tq .

The dependent variable is the “free prices” component of headline inflation because

administered prices have a different price dynamics, partially obeying contract rules. Note

that the estimated pass-through refers to the transmission from exchange rate change in the

previous quarter to the current inflation, that is, it captures only the short-run effect of

exchange rate movements.

To enable the joint estimation, the previous equations become:

( )( )( )( ) tttttttt

tttttttLt

qIyeE

qIyeE

εταπαπααπα

ταπαπααπαπ

+≥++Δ+−−+

+⟨−++Δ+−−+=

−−−−+

−−−−+

[)()1(

[1)()1(

124

*11

221

22

211

21

114

*11

121

12

111

11 . (14)

Based on theoretical indications for a nonlinear exchange rate pass-through, we

evaluate three threshold variables: i) business cycle, measured by the output gap; ii)

magnitude of nominal exchange rate changes; and iii) a measure of exchange rate volatility.

We use quarterly data from 1995:1 through 2005:4 and estimate using 2SLS, with

instrumental variables for the inflation expectations term.

The first estimated specification has the output gap as the threshold variable. In this

model, all parameters, except for that of the output gap, are subject to regime switching.7

The estimation results are the following (p-values in parentheses):

6 The output gap used in the estimation was generated using a production function model. See, for example, the box "Methodologies for estimating the potential output" in Banco Central do Brasil (2003) and Muinhos and Alves (2003) for a description of the methodology. 7 We do not allow the coefficient on output gap to change because we want to capture nonlinearities in the pass-through.

11

)00.0()78.0()23.0()00.0(%89.124.0)(00.025.075.0 12

*1111 −⟨+π+Δ+π+π=π −−−−−+ ttttttt

Lt yifyeE

)00.0()03.0()11.0()02.0(%89.124.0)(09.033.058.0 12

*1111 −≥+π+Δ+π+π=π −−−−−+ ttttttt

Lt yifyeE

Sample period: 1995:1–2005:4 Standard errors estimated using Newey-West consistent estimators P-values in parentheses Impulse dummy variable for 1999:1: 0.02, p-value: 0.00 Instrumental variables: const., dummy variable, 1−tπ , 2−tπ , 1−Δ te , 2−Δ te , *

1−tπ , *2−tπ , 2−ty

R-squared: 0.50 Adjusted R-squared: 0.43 Breusch-Godfrey Serial Correlation LM test, p-values: 1 lag: 0.54, 4 lags: 0.33 White Heteroskedasticity Test, p-value: 0.27 Jarque-Bera Normality Test, p-value: 0.57 Wald test 2

212 αα = , p-value: 0.04

According to the estimation results, there is a nonlinearity in the pass-through term

related to the business cycle: the exchange rate pass-through is not statistically different

from zero in the regime when the economy is below the threshold, whereas it is around 9%

when economic activity is higher. According to the Wald test, we reject the null that the

two pass-through coefficients are equal. The exchange rate pass-through is significantly

greater when output is above some threshold8, estimated at 1.89% below the potential

output. This means that, during an economic slowdown, an exchange rate variation will

have a smaller impact on domestic prices. This is usually pointed as one of the factors that

limited the pass-through in Brazil during the 1999 exchange rate crisis. One limitation of

this result is its implication that exchange rate appreciations have a higher pass-through

when the economy is booming than when the output gap is below the threshold.

The other parameter estimates are in line with those found in the literature using

models without a threshold variable. Except for the backward-looking term, all coefficients

are statistically significant at 5%. In addition, the estimated value for the threshold splits the

sample into two approximately equal parts (19 observations when 89.11 −<−ty %, and 25

when 89.11 −≥−ty %). This means that, although the sample size is not large, none of the

8 This result is in line with those in Goldfajn and Werlang (2000), and Carneiro, Monteiro and Wu (2002).

12

regimes was estimated with an extremely low number of observations.9 Actually, we have

tried several specifications, using different instruments for the expectations term, and the

results were robust.

The second estimated model considers nominal exchange rate changes as the

threshold variable. Similarly to the previous model, all parameters are allowed to vary with

the regime change, except for the output gap parameter, kept constant in both regimes. The

estimation results are the following10:

)01.0()31.0()00.0()00.0(%10.227.0)(02.040.058.0 11

*1111 ⟨Δ+π+Δ+π+π=π −−−−−+ ttttttt

Lt eifyeE

)01.0()03.0()07.0()10.0(%10.227.0)(11.045.044.0 11

*1111 ≥Δ+π+Δ+π+π=π −−−−−+ ttttttt

Lt eifyeE .

Sample period: 1995:1–2005:4 Standard errors estimated using Newey-West consistent estimators P-values in parentheses Impulse dummy variable for 1999:1: 0.03, p-value: 0.08 Instrument variables: const., dummy var., 1−tπ , 2−tπ , 3−tπ , 1−Δ te , 2−Δ te , *

1−tπ , *2−tπ , 2−ty

R-squared: 0.50 Adjusted R-squared: 0.43 Breusch-Godfrey Serial Correlation LM test, p-values: 1 lag: 1.00, 4 lags: 0.38 White Heteroskedasticity Test, p-value: 0.69 Jarque-Bera Normality Test, p-value: 0.31 Wald test 2

212 αα = , p-value: 0.06

Those results indicate that the short-run effect of exchange rate changes on inflation

is asymmetric. In the case of large exchange rate depreciations, the estimated pass-through

for the following quarter is around 11%, whereas appreciations or small depreciations do

not have a statistically significant effect. The Wald test rejects the null hypothesis that both

coefficients are equal. Therefore, the pass-through is greater when quarter-on-quarter

depreciations are equal to or larger than 2.1%. Although the results on the effect of an

9 Including the period previous to the launch of the Real Plan is not recommendable because the inflation dynamics in a high inflation regime is substantially different, distorting the estimation. 10 In that specification, we have used for the backward-looking inflation and output gap terms the average of

their values at t-1 and t-2, that is, ( ) 2/211

At

Att −

+−

=− πππ and ( ) 2/211

At

yAt

yty−

+−

=− , where the

superscript A means actual values. That specification generates better fitting.

13

appreciation in the previous quarter on current inflation were not statistically significant,

we should not infer that appreciations are not transmitted to prices. This transmission can

take place with more lags than in the case of depreciation.

As before, the estimated parameters are robust with respect to the instruments used

and are statistically significant at 5% (except the coefficient on lagged inflation when

%10.21 ≥Δ −te ). Moreover, the number of observations in each regime was reasonably

balanced (15 observations in the large depreciation regime, and 29 in the other) and the

estimated values for the coefficients are close to those reported in the literature. Note that in

both estimations the forward-looking inflation coefficient is greater than the backward-

looking component.

Since the estimated threshold is not zero, its slightly positive value (close to 2%)

suggests the presence of menu costs or some adjustment costs of prices, where small

exchange rate changes are not promptly transmitted to prices. If price changes are costly, a

small change in the currency value can be accommodated within the markup margin. In this

case, firms tend to postpone their decisions, adjusting their markup in the short-run.

However, if exchange rate changes surpass some limit, even if the change is temporary, the

costs of not adjusting prices are higher, leading firms to change prices more rapidly.

Consequently, the presence of menu costs increases the possibility that firms will adjust

price mainly if exchange rate changes surpass some threshold, resulting in an asymmetric

pass-through related to small and large exchange rate changes.

Furthermore, pricing-to-market theory delivers an explanation for a partial pass-

through and for an asymmetry related to appreciations and depreciations in the exchange

rate. Consider the domestic sector formed by subsidiaries of foreign firms that produce

abroad and sell their products internally. In the case of an exchange rate depreciation, those

firms have three options: i) to reduce their markup to keep stable the price in local currency

(absence of pass-through); ii) to keep their markup, increasing the price charged in local

currency to reflect completely the exchange rate change (complete pass-through), which

may imply a market share reduction; or iii) a combination of the previous two possibilities

(partial pass-through).

When subsidiary firms are trying to build up or keep their market shares, a local

currency depreciation results in a lower pass-through than that when there is an

14

appreciation. Nevertheless, if the depreciation of the domestic currency is high, there is less

room for markup adjustments, and at least partially the depreciation is transmitted to

domestic prices to avoid losses. In the case of appreciation, firms' profits increase if they

keep constant domestic prices, which could result in a longer period to adjust prices

downwards. The extension of these effects on the price level in the economy depends on

the price-elasticity of demand for these firms’ goods and on the degree of openness of the

economy. In addition, if the firms that produce abroad face a restriction on their production

capacity, an exchange rate appreciation can result in a lower pass-through than in the case

of a depreciation. The restriction capacity limits the fall in domestic price that the

appreciation could generate.

The previous estimated models do not make any distinction between the pre-1999

period, when the exchange rate was managed – following in practice a crawling peg system

– and the following period of a floating rate. In fact, when we include a step dummy into

the exchange rate term, the results deteriorate substantially in terms of signs and statistical

significance of the parameters. This result may be related to the increase in the number of

parameters to be estimated when we include a dummy variable, reducing the degree of

freedom of the estimation.

Because of those limitations, we have estimated a third model, using exchange rate

volatility as the threshold variable. This estimation would tend to resolve, at least partially,

the problem of the separation of the exchange rate regimes (before and after January 1999)

because the threshold estimation tends to classify the observations of the managed system

period into the low volatility regime. In principle, the low volatility estimated regime could

also contain observations from when the exchange rate was relatively stable during the float

period.

In addition, that estimation aims to capture the inflationary effects in two different

situations: i) when agents perceive exchange rate changes as transitory; and ii) when they

perceive them as permanent. When agents consider exchange rate variations as more

permanent, more promptly they will be transmitted to prices. Our assumption is that the

probability that agents consider changes as permanent is higher in periods of low exchange

15

rate volatility and smaller in periods of greater volatility.11 Thus, we would expect a lower

pass-through in periods of higher exchange rate instability.

We have used the standard deviation of daily changes in the exchange rate within

each quarter as the measure of volatility. The estimation results were the following12:

)00.0()21.0()83.0()74.0(%07.031.0)(80.005.015.0 1,1

*1111 ⟨++Δ++= −−−−−+ tetttttt

Lt ifyeE σππππ

)00.0()05.0()00.0()07.0(%07.031.0)(07.063.030.0 1,1

*1111 ≥++Δ++= −−−−−+ tetttttt

Lt ifyeE σππππ

.

Sample period: 1995:1–2005:4 Standard errors estimated using Newey-West consistent estimators P-values in parentheses Impulse dummy variable for 1999:1: 0.03, p-value: 0.00 Instrumental variables: const., dummy variable, 1−tπ , 2−tπ , 1−Δ te , 2−Δ te , *

1−tπ , *2−tπ , 1−ty

R-squared: 0.52 Adjusted R-squared: 0.45 Breusch-Godfrey Serial Correlation LM test, p-values: 1 lag: 0.69, 4 lags: 0.22 White Heteroskedasticity Test, p-value: 0.31 Jarque-Bera Normality Test, p-value: 0.21 Wald test 2

212 αα = , p-value: 0.25

In terms of magnitude, the point estimates indicate a greater pass-through in low

volatility periods than in high volatility moments (80% and 7%, respectively). However,

the estimated pass-through is not statistically significant in the low volatility regime,

although it is significant in the other regime and the parameter values are close to those

reported in the literature for the periods of managed and floating exchange rates.13 The

resulting sample division assigned most of the observations of the managed system to the

11 Albuquerque and Portugal (2006), for example, explore the relationship between exchange rate volatility and inflation in Brazil, using a bivariate GARCH model. 12 In that specification, we have used for the backward-looking inflation term the average of their values at t-

1, t-2 and t-3, that is, ( ) 3/3211

At

At

Att −

+−

+−

=− ππππ , and for the output gap term, the average at t-1 and t-

2, that is, ( ) 2/211

At

yAt

yty−

+−

=− , where the superscript A means actual values. That specification has

generated better fitting.

16

low volatility regime. The observations corresponding to values below the threshold

comprise the 1995:4–1998:2 period. Nevertheless, according to the Wald test, we cannot

reject the null that both coefficients are equal, and the results of this Phillips curve

specification are less robust than those of the two previous models. Therefore, these results

should be considered with more caution.

Figure 1 illustrates the results concerning the first model estimated. It presents the

quarterly free price inflation, the exchange rate change (lagged one period), and a line that

indicates the threshold value (-1.89%) of output gap. This line separates the periods when

output gap is above and below the threshold. We point out some periods, described in Table

1, in which the estimated model can explain, at least partially, the relation between

exchange rate changes and free price inflation. The table records the corresponding values,

besides including headline inflation (measured by IPCA).

Figure 1 – Free price inflation, exchange rate changes and the output gap

-3 -2 -1 0 1 2 3 4 5 6 7

I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III 1998 1999 2000 2001 2002 2003 2004 2005

Free

pric

e in

flatio

n (%

)

-35

-20

-5

10

25

40

Exc

hang

e ra

te c

hang

e (%

)

Free price inflation Period output gap above the thr eshol d

Period output gap bel ow the threshold Exchange rate change (t-1)

d – + d d + d + a +

13 Muinhos and Alves (2003), por instance, have found a coefficient reduction from 51% to 6% after the change in the exchange rate regime, and Albuquerque and Portugal (2005), using a Kalman filter model, have estimated parameters values around 42% and 4%, respectively.

17

Table 1 – Inflation and exchange rate changes in selected periods

1999: II d – 2.88 1.05 2.59 0.49 39.332000:III d + 0.66 3.18 0.71 1.93 1.642001:II d + 1.42 1.52 1.42 1.40 4.392001:III d + 1.52 2.33 1.40 1.41 12.692002:III d + 1.44 2.58 0.62 2.56 4.872002:IV d + 2.58 6.56 2.56 6.34 22.302004:IV a + 1.94 2.00 1.35 1.31 -2.302005:I a + 2.00 1.79 1.31 1.72 -6.802005:II a + 1.79 1.34 1.72 1.40 -4.42Note: d+ means depreciation with booming

d– means depreciation with recession

a+ means appreciation with booming

a– means appreciation with recession

The exchange rate change is calculated based on the quarterly exchange rate average

Period CharacteristicHeadline inflation

in t

Exchange rate change

in t-1

Headline inflation

in t-1

Free price inflation

in t-1

Free price inflation

in t

In the second quarter of 1999 (immediately after the float), for instance, in spite of

the 39% exchange rate depreciation in the previous quarter, free price inflation was only

0.49% and the headline inflation stood at 1.05%, both below the previous quarter values. In

that period, the output gap was below the estimated threshold (economic slowdown), which

implies, according to the model, a low pass-through to inflation. The depreciations in the

third quarter of 2000 and during 2001, in turn, were followed by higher increases in the

inflation rate. In that period, the output gap was higher than the estimated threshold.

In mid-2002, when the economy was growing faster, a strong depreciation was

accompanied by a great inflation rise. In the last quarter, for instance, when the

depreciation in the previous quarter reached 22%, free price inflation went from 2.56% to

6.34%, and headline inflation rose from 2.58% to 6.56%.

On the other hand, although inflation fell along 2005, it did not follow so promptly

the exchange rate appreciation started in the last quarter of 2004. One possible explanation

lies on the asymmetry of the short-run pass-through with respect to appreciation and

depreciation, put in evidence by the model with the threshold given by exchange rate

changes. Furthermore, initial movements of appreciation were possibly not perceived

immediately as having longer duration, postponing the effect on prices. In fact, the model

estimates the short-run pass-through, that is, the effect on current inflation of the change in

18

the exchange rate in the previous quarter. The appreciation contributed for the reduction in

inflation, but probably with lags greater than one quarter.

4. Conclusions

This paper explores the possibility of the presence of a nonlinear pass-through from

the exchange rate to inflation in Brazil. We have estimated models for the Phillips curve

combined with the methodology of threshold models. In these models, the parameter values

depend on which regime the economy is, which are determined endogenously by means of

an observed variable.

The choice of variables used was based on the possible sources of nonlinearity of

the pass-through reported in the literature. In particular, we have examined three sources: i)

business cycle; ii) exchange rate changes; and iii) exchange rate volatility.

The estimations indicate the presence of nonlinear mechanisms in the short-run

pass-through in Brazil. The short-run pass-through is higher when the economy is booming,

when the exchange rate depreciates above some threshold, and when exchange rate

volatility is lower. These results have important implications for monetary policy and are

possibly related to a pricing-to-market behavior, menu costs to change prices, and

uncertainty about the degree of persistence of exchange rate changes.

19

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22

Banco Central do Brasil

Trabalhos para Discussão Os Trabalhos para Discussão podem ser acessados na internet, no formato PDF,

no endereço: http://www.bc.gov.br

Working Paper Series

Working Papers in PDF format can be downloaded from: http://www.bc.gov.br

1 Implementing Inflation Targeting in Brazil

Joel Bogdanski, Alexandre Antonio Tombini and Sérgio Ribeiro da Costa Werlang

Jul/2000

2 Política Monetária e Supervisão do Sistema Financeiro Nacional no Banco Central do Brasil Eduardo Lundberg Monetary Policy and Banking Supervision Functions on the Central Bank Eduardo Lundberg

Jul/2000

Jul/2000

3 Private Sector Participation: a Theoretical Justification of the Brazilian Position Sérgio Ribeiro da Costa Werlang

Jul/2000

4 An Information Theory Approach to the Aggregation of Log-Linear Models Pedro H. Albuquerque

Jul/2000

5 The Pass-Through from Depreciation to Inflation: a Panel Study Ilan Goldfajn and Sérgio Ribeiro da Costa Werlang

Jul/2000

6 Optimal Interest Rate Rules in Inflation Targeting Frameworks José Alvaro Rodrigues Neto, Fabio Araújo and Marta Baltar J. Moreira

Jul/2000

7 Leading Indicators of Inflation for Brazil Marcelle Chauvet

Sep/2000

8 The Correlation Matrix of the Brazilian Central Bank’s Standard Model for Interest Rate Market Risk José Alvaro Rodrigues Neto

Sep/2000

9 Estimating Exchange Market Pressure and Intervention Activity Emanuel-Werner Kohlscheen

Nov/2000

10 Análise do Financiamento Externo a uma Pequena Economia Aplicação da Teoria do Prêmio Monetário ao Caso Brasileiro: 1991–1998 Carlos Hamilton Vasconcelos Araújo e Renato Galvão Flôres Júnior

Mar/2001

11 A Note on the Efficient Estimation of Inflation in Brazil Michael F. Bryan and Stephen G. Cecchetti

Mar/2001

12 A Test of Competition in Brazilian Banking Márcio I. Nakane

Mar/2001

23

13 Modelos de Previsão de Insolvência Bancária no Brasil Marcio Magalhães Janot

Mar/2001

14 Evaluating Core Inflation Measures for Brazil Francisco Marcos Rodrigues Figueiredo

Mar/2001

15 Is It Worth Tracking Dollar/Real Implied Volatility? Sandro Canesso de Andrade and Benjamin Miranda Tabak

Mar/2001

16 Avaliação das Projeções do Modelo Estrutural do Banco Central do Brasil para a Taxa de Variação do IPCA Sergio Afonso Lago Alves Evaluation of the Central Bank of Brazil Structural Model’s Inflation Forecasts in an Inflation Targeting Framework Sergio Afonso Lago Alves

Mar/2001

Jul/2001

17 Estimando o Produto Potencial Brasileiro: uma Abordagem de Função de Produção Tito Nícias Teixeira da Silva Filho Estimating Brazilian Potential Output: a Production Function Approach Tito Nícias Teixeira da Silva Filho

Abr/2001

Aug/2002

18 A Simple Model for Inflation Targeting in Brazil Paulo Springer de Freitas and Marcelo Kfoury Muinhos

Apr/2001

19 Uncovered Interest Parity with Fundamentals: a Brazilian Exchange Rate Forecast Model Marcelo Kfoury Muinhos, Paulo Springer de Freitas and Fabio Araújo

May/2001

20 Credit Channel without the LM Curve Victorio Y. T. Chu and Márcio I. Nakane

May/2001

21 Os Impactos Econômicos da CPMF: Teoria e Evidência Pedro H. Albuquerque

Jun/2001

22 Decentralized Portfolio Management Paulo Coutinho and Benjamin Miranda Tabak

Jun/2001

23 Os Efeitos da CPMF sobre a Intermediação Financeira Sérgio Mikio Koyama e Márcio I. Nakane

Jul/2001

24 Inflation Targeting in Brazil: Shocks, Backward-Looking Prices, and IMF Conditionality Joel Bogdanski, Paulo Springer de Freitas, Ilan Goldfajn and Alexandre Antonio Tombini

Aug/2001

25 Inflation Targeting in Brazil: Reviewing Two Years of Monetary Policy 1999/00 Pedro Fachada

Aug/2001

26 Inflation Targeting in an Open Financially Integrated Emerging Economy: the Case of Brazil Marcelo Kfoury Muinhos

Aug/2001

27

Complementaridade e Fungibilidade dos Fluxos de Capitais Internacionais Carlos Hamilton Vasconcelos Araújo e Renato Galvão Flôres Júnior

Set/2001

24

28

Regras Monetárias e Dinâmica Macroeconômica no Brasil: uma Abordagem de Expectativas Racionais Marco Antonio Bonomo e Ricardo D. Brito

Nov/2001

29 Using a Money Demand Model to Evaluate Monetary Policies in Brazil Pedro H. Albuquerque and Solange Gouvêa

Nov/2001

30 Testing the Expectations Hypothesis in the Brazilian Term Structure of Interest Rates Benjamin Miranda Tabak and Sandro Canesso de Andrade

Nov/2001

31 Algumas Considerações sobre a Sazonalidade no IPCA Francisco Marcos R. Figueiredo e Roberta Blass Staub

Nov/2001

32 Crises Cambiais e Ataques Especulativos no Brasil Mauro Costa Miranda

Nov/2001

33 Monetary Policy and Inflation in Brazil (1975-2000): a VAR Estimation André Minella

Nov/2001

34 Constrained Discretion and Collective Action Problems: Reflections on the Resolution of International Financial Crises Arminio Fraga and Daniel Luiz Gleizer

Nov/2001

35 Uma Definição Operacional de Estabilidade de Preços Tito Nícias Teixeira da Silva Filho

Dez/2001

36 Can Emerging Markets Float? Should They Inflation Target? Barry Eichengreen

Feb/2002

37 Monetary Policy in Brazil: Remarks on the Inflation Targeting Regime, Public Debt Management and Open Market Operations Luiz Fernando Figueiredo, Pedro Fachada and Sérgio Goldenstein

Mar/2002

38 Volatilidade Implícita e Antecipação de Eventos de Stress: um Teste para o Mercado Brasileiro Frederico Pechir Gomes

Mar/2002

39 Opções sobre Dólar Comercial e Expectativas a Respeito do Comportamento da Taxa de Câmbio Paulo Castor de Castro

Mar/2002

40 Speculative Attacks on Debts, Dollarization and Optimum Currency Areas Aloisio Araujo and Márcia Leon

Apr/2002

41 Mudanças de Regime no Câmbio Brasileiro Carlos Hamilton V. Araújo e Getúlio B. da Silveira Filho

Jun/2002

42 Modelo Estrutural com Setor Externo: Endogenização do Prêmio de Risco e do Câmbio Marcelo Kfoury Muinhos, Sérgio Afonso Lago Alves e Gil Riella

Jun/2002

43 The Effects of the Brazilian ADRs Program on Domestic Market Efficiency Benjamin Miranda Tabak and Eduardo José Araújo Lima

Jun/2002

25

44 Estrutura Competitiva, Produtividade Industrial e Liberação Comercial no Brasil Pedro Cavalcanti Ferreira e Osmani Teixeira de Carvalho Guillén

Jun/2002

45 Optimal Monetary Policy, Gains from Commitment, and Inflation Persistence André Minella

Aug/2002

46 The Determinants of Bank Interest Spread in Brazil Tarsila Segalla Afanasieff, Priscilla Maria Villa Lhacer and Márcio I. Nakane

Aug/2002

47 Indicadores Derivados de Agregados Monetários Fernando de Aquino Fonseca Neto e José Albuquerque Júnior

Set/2002

48 Should Government Smooth Exchange Rate Risk? Ilan Goldfajn and Marcos Antonio Silveira

Sep/2002

49 Desenvolvimento do Sistema Financeiro e Crescimento Econômico no Brasil: Evidências de Causalidade Orlando Carneiro de Matos

Set/2002

50 Macroeconomic Coordination and Inflation Targeting in a Two-Country Model Eui Jung Chang, Marcelo Kfoury Muinhos and Joanílio Rodolpho Teixeira

Sep/2002

51 Credit Channel with Sovereign Credit Risk: an Empirical Test Victorio Yi Tson Chu

Sep/2002

52 Generalized Hyperbolic Distributions and Brazilian Data José Fajardo and Aquiles Farias

Sep/2002

53 Inflation Targeting in Brazil: Lessons and Challenges André Minella, Paulo Springer de Freitas, Ilan Goldfajn and Marcelo Kfoury Muinhos

Nov/2002

54 Stock Returns and Volatility Benjamin Miranda Tabak and Solange Maria Guerra

Nov/2002

55 Componentes de Curto e Longo Prazo das Taxas de Juros no Brasil Carlos Hamilton Vasconcelos Araújo e Osmani Teixeira de Carvalho de Guillén

Nov/2002

56 Causality and Cointegration in Stock Markets: the Case of Latin America Benjamin Miranda Tabak and Eduardo José Araújo Lima

Dec/2002

57 As Leis de Falência: uma Abordagem Econômica Aloisio Araujo

Dez/2002

58 The Random Walk Hypothesis and the Behavior of Foreign Capital Portfolio Flows: the Brazilian Stock Market Case Benjamin Miranda Tabak

Dec/2002

59 Os Preços Administrados e a Inflação no Brasil Francisco Marcos R. Figueiredo e Thaís Porto Ferreira

Dez/2002

60 Delegated Portfolio Management Paulo Coutinho and Benjamin Miranda Tabak

Dec/2002

26

61 O Uso de Dados de Alta Freqüência na Estimação da Volatilidade e do Valor em Risco para o Ibovespa João Maurício de Souza Moreira e Eduardo Facó Lemgruber

Dez/2002

62 Taxa de Juros e Concentração Bancária no Brasil Eduardo Kiyoshi Tonooka e Sérgio Mikio Koyama

Fev/2003

63 Optimal Monetary Rules: the Case of Brazil Charles Lima de Almeida, Marco Aurélio Peres, Geraldo da Silva e Souza and Benjamin Miranda Tabak

Feb/2003

64 Medium-Size Macroeconomic Model for the Brazilian Economy Marcelo Kfoury Muinhos and Sergio Afonso Lago Alves

Feb/2003

65 On the Information Content of Oil Future Prices Benjamin Miranda Tabak

Feb/2003

66 A Taxa de Juros de Equilíbrio: uma Abordagem Múltipla Pedro Calhman de Miranda e Marcelo Kfoury Muinhos

Fev/2003

67 Avaliação de Métodos de Cálculo de Exigência de Capital para Risco de Mercado de Carteiras de Ações no Brasil Gustavo S. Araújo, João Maurício S. Moreira e Ricardo S. Maia Clemente

Fev/2003

68 Real Balances in the Utility Function: Evidence for Brazil Leonardo Soriano de Alencar and Márcio I. Nakane

Feb/2003

69 r-filters: a Hodrick-Prescott Filter Generalization Fabio Araújo, Marta Baltar Moreira Areosa and José Alvaro Rodrigues Neto

Feb/2003

70 Monetary Policy Surprises and the Brazilian Term Structure of Interest Rates Benjamin Miranda Tabak

Feb/2003

71 On Shadow-Prices of Banks in Real-Time Gross Settlement Systems Rodrigo Penaloza

Apr/2003

72 O Prêmio pela Maturidade na Estrutura a Termo das Taxas de Juros Brasileiras Ricardo Dias de Oliveira Brito, Angelo J. Mont'Alverne Duarte e Osmani Teixeira de C. Guillen

Maio/2003

73 Análise de Componentes Principais de Dados Funcionais – Uma Aplicação às Estruturas a Termo de Taxas de Juros Getúlio Borges da Silveira e Octavio Bessada

Maio/2003

74 Aplicação do Modelo de Black, Derman & Toy à Precificação de Opções Sobre Títulos de Renda Fixa Octavio Manuel Bessada Lion, Carlos Alberto Nunes Cosenza e César das Neves

Maio/2003

75 Brazil’s Financial System: Resilience to Shocks, no Currency Substitution, but Struggling to Promote Growth Ilan Goldfajn, Katherine Hennings and Helio Mori

Jun/2003

27

76 Inflation Targeting in Emerging Market Economies Arminio Fraga, Ilan Goldfajn and André Minella

Jun/2003

77 Inflation Targeting in Brazil: Constructing Credibility under Exchange Rate Volatility André Minella, Paulo Springer de Freitas, Ilan Goldfajn and Marcelo Kfoury Muinhos

Jul/2003

78 Contornando os Pressupostos de Black & Scholes: Aplicação do Modelo de Precificação de Opções de Duan no Mercado Brasileiro Gustavo Silva Araújo, Claudio Henrique da Silveira Barbedo, Antonio Carlos Figueiredo, Eduardo Facó Lemgruber

Out/2003

79 Inclusão do Decaimento Temporal na Metodologia Delta-Gama para o Cálculo do VaR de Carteiras Compradas em Opções no Brasil Claudio Henrique da Silveira Barbedo, Gustavo Silva Araújo, Eduardo Facó Lemgruber

Out/2003

80 Diferenças e Semelhanças entre Países da América Latina: uma Análise de Markov Switching para os Ciclos Econômicos de Brasil e Argentina Arnildo da Silva Correa

Out/2003

81 Bank Competition, Agency Costs and the Performance of the Monetary Policy Leonardo Soriano de Alencar and Márcio I. Nakane

Jan/2004

82 Carteiras de Opções: Avaliação de Metodologias de Exigência de Capital no Mercado Brasileiro Cláudio Henrique da Silveira Barbedo e Gustavo Silva Araújo

Mar/2004

83 Does Inflation Targeting Reduce Inflation? An Analysis for the OECD Industrial Countries Thomas Y. Wu

May/2004

84 Speculative Attacks on Debts and Optimum Currency Area: a Welfare Analysis Aloisio Araujo and Marcia Leon

May/2004

85 Risk Premia for Emerging Markets Bonds: Evidence from Brazilian Government Debt, 1996-2002 André Soares Loureiro and Fernando de Holanda Barbosa

May/2004

86 Identificação do Fator Estocástico de Descontos e Algumas Implicações sobre Testes de Modelos de Consumo Fabio Araujo e João Victor Issler

Maio/2004

87 Mercado de Crédito: uma Análise Econométrica dos Volumes de Crédito Total e Habitacional no Brasil Ana Carla Abrão Costa

Dez/2004

88 Ciclos Internacionais de Negócios: uma Análise de Mudança de Regime Markoviano para Brasil, Argentina e Estados Unidos Arnildo da Silva Correa e Ronald Otto Hillbrecht

Dez/2004

89 O Mercado de Hedge Cambial no Brasil: Reação das Instituições Financeiras a Intervenções do Banco Central Fernando N. de Oliveira

Dez/2004

28

90 Bank Privatization and Productivity: Evidence for Brazil Márcio I. Nakane and Daniela B. Weintraub

Dec/2004

91 Credit Risk Measurement and the Regulation of Bank Capital and Provision Requirements in Brazil – A Corporate Analysis Ricardo Schechtman, Valéria Salomão Garcia, Sergio Mikio Koyama and Guilherme Cronemberger Parente

Dec/2004

92

Steady-State Analysis of an Open Economy General Equilibrium Model for Brazil Mirta Noemi Sataka Bugarin, Roberto de Goes Ellery Jr., Victor Gomes Silva, Marcelo Kfoury Muinhos

Apr/2005

93 Avaliação de Modelos de Cálculo de Exigência de Capital para Risco Cambial Claudio H. da S. Barbedo, Gustavo S. Araújo, João Maurício S. Moreira e Ricardo S. Maia Clemente

Abr/2005

94 Simulação Histórica Filtrada: Incorporação da Volatilidade ao Modelo Histórico de Cálculo de Risco para Ativos Não-Lineares Claudio Henrique da Silveira Barbedo, Gustavo Silva Araújo e Eduardo Facó Lemgruber

Abr/2005

95 Comment on Market Discipline and Monetary Policy by Carl Walsh Maurício S. Bugarin and Fábia A. de Carvalho

Apr/2005

96 O que É Estratégia: uma Abordagem Multiparadigmática para a Disciplina Anthero de Moraes Meirelles

Ago/2005

97 Finance and the Business Cycle: a Kalman Filter Approach with Markov Switching Ryan A. Compton and Jose Ricardo da Costa e Silva

Aug/2005

98 Capital Flows Cycle: Stylized Facts and Empirical Evidences for Emerging Market Economies Helio Mori e Marcelo Kfoury Muinhos

Aug/2005

99 Adequação das Medidas de Valor em Risco na Formulação da Exigência de Capital para Estratégias de Opções no Mercado Brasileiro Gustavo Silva Araújo, Claudio Henrique da Silveira Barbedo,e Eduardo Facó Lemgruber

Set/2005

100 Targets and Inflation Dynamics Sergio A. L. Alves and Waldyr D. Areosa

Oct/2005

101 Comparing Equilibrium Real Interest Rates: Different Approaches to Measure Brazilian Rates Marcelo Kfoury Muinhos and Márcio I. Nakane

Mar/2006

102 Judicial Risk and Credit Market Performance: Micro Evidence from Brazilian Payroll Loans Ana Carla A. Costa and João M. P. de Mello

Apr/2006

103 The Effect of Adverse Supply Shocks on Monetary Policy and Output Maria da Glória D. S. Araújo, Mirta Bugarin, Marcelo Kfoury Muinhos and Jose Ricardo C. Silva

Apr/2006

29

104 Extração de Informação de Opções Cambiais no Brasil Eui Jung Chang e Benjamin Miranda Tabak

Abr/2006

105 Representing Roomate’s Preferences with Symmetric Utilities José Alvaro Rodrigues-Neto

Apr/2006

106 Testing Nonlinearities Between Brazilian Exchange Rates and Inflation Volatilities Cristiane R. Albuquerque and Marcelo Portugal

May/2006

107 Demand for Bank Services and Market Power in Brazilian Banking Márcio I. Nakane, Leonardo S. Alencar and Fabio Kanczuk

Jun/2006

108 O Efeito da Consignação em Folha nas Taxas de Juros dos Empréstimos Pessoais Eduardo A. S. Rodrigues, Victorio Chu, Leonardo S. Alencar e Tony Takeda

Jun/2006

109 The Recent Brazilian Disinflation Process and Costs Alexandre A. Tombini and Sergio A. Lago Alves

Jun/2006

110 Fatores de Risco e o Spread Bancário no Brasil Fernando G. Bignotto e Eduardo Augusto de Souza Rodrigues

Jul/2006

111 Avaliação de Modelos de Exigência de Capital para Risco de Mercado do Cupom Cambial Alan Cosme Rodrigues da Silva, João Maurício de Souza Moreira e Myrian Beatriz Eiras das Neves

Jul/2006

112 Interdependence and Contagion: an Analysis of Information Transmission in Latin America's Stock Markets Angelo Marsiglia Fasolo

Jul/2006

113 Investigação da Memória de Longo Prazo da Taxa de Câmbio no Brasil Sergio Rubens Stancato de Souza, Benjamin Miranda Tabak e Daniel O. Cajueiro

Ago/2006

114 The Inequality Channel of Monetary Transmission Marta Areosa and Waldyr Areosa

Aug/2006

115 Myopic Loss Aversion and House-Money Effect Overseas: an experimental approach José L. B. Fernandes, Juan Ignacio Peña and Benjamin M. Tabak

Sep/2006

116 Out-Of-The-Money Monte Carlo Simulation Option Pricing: the join use of Importance Sampling and Descriptive Sampling Jaqueline Terra Moura Marins, Eduardo Saliby and Joséte Florencio do Santos

Sep/2006

117 An Analysis of Off-Site Supervision of Banks’ Profitability, Risk and Capital Adequacy: a portfolio simulation approach applied to brazilian banks Theodore M. Barnhill, Marcos R. Souto and Benjamin M. Tabak

Sep/2006

118 Contagion, Bankruptcy and Social Welfare Analysis in a Financial Economy with Risk Regulation Constraint Aloísio P. Araújo and José Valentim M. Vicente

Oct/2006

30

119 A Central de Risco de Crédito no Brasil: uma análise de utilidade de informação Ricardo Schechtman

Out/2006

120 Forecasting Interest Rates: an application for Brazil Eduardo J. A. Lima, Felipe Luduvice and Benjamin M. Tabak

Oct/2006

121 The Role of Consumer’s Risk Aversion on Price Rigidity Sergio A. Lago Alves and Mirta N. S. Bugarin

Nov/2006