ISSN 1518-3548 Working Paper Series Medium-Size Macroeconomic Model for the Brazilian Economy Marcelo Kfoury Muinhos and Sergio Afonso Lago Alves February, 2003 ISSN 1518-3548 CGC 00.038.166/0001-05 Working Paper Series Brasília n. 64 Feb 2003 p. 1 – 48 Working Paper Series Edited by: Research Department (Depep) (E-mail: workingpaper@bcb.gov.br) Reproduction permitted only if source is stated as follows: Working Paper Series n. 64 Authorized by Ilan Goldfajn (Deputy Governor for Economic Policy). General Control of Subscription: Banco Central do Brasil Demap/Disud/Subip SBS – Quadra 3 – Bloco B – Edifício -Sede – 2º subsolo 70074-900 Brasília – DF – Brazil Phone: (5561) 414-1392 Fax: (5561) 414-3165 The views expressed in this work are those of the authors and do not reflect those of the Banco Central or its members. Although these Working Papers often represent preliminary work, citation of source is required when used or reproduced. As opiniões expressas neste trabalho são exclusivamente do(s) autor(es) e não refletem a visão do Banco Central do Brasil. Ainda que este artigo represente trabalho preliminar, citação da fonte é requerida mesmo quando reproduzido parcialmente. Banco Central do Brasil Information Bureau Address: Secre/Surel/Dinfo SBS – Quadra 3 – Bloco B Edifício -Sede, 2º subsolo 70074-900 Brasília – DF Phones: (5561) 414 (....) 2401, 2402, 2403, 2404, 2405, 2406 DDG: 0800 992345 FAX: (5561) 321-9453 Internet: http://www.bcb.gov.br E-mails: cap.secre@bcb.gov.br dinfo.secre@bcb.gov.br 0HGLXP6L]H0DFURHFRQRPLF0RGHO IRUWKH%UD]LOLDQ(FRQRP\   0DUFHOR.IRXU\0XLQKRV   6HUJLR$IRQVR/DJR$OYHV    $EVWUDFW  This paper presents a medium-scale macroeconomic model of the Brazilian economy with more than 30 equations. Potential output is derived from a Cobb-Douglas production function, while the demand side is divided into estimated equations for: household consumption, investment in machinery and construction, government spending and net exports. The estimated Phillips curve has an interesting feature: a step dummy variable captures the macroeconomic break in pass-through that occurred after the change of the exchange rate regime in 1999. There are long-run equilibrium conditions for the external and fiscal debt and also for the real interest rate. External and supply shocks were simulated in order to generate impulse responses for the medium size model. Key words: macroeconomic model, interest rate equilibrium, and potential output. JEL Classification: E12, E27, F43, F47 * We would like to thank Gil Riella for his outstand help in running the model in Matlab. Flávia Mourão Graminho, Eduardo Loyo, Shad Turney and Andrew Levin also helped us in the estimations and with suggestions. The views expressed in this work are those of the authors and do not reflect those of the Banco Central do Brasil or its members. ** Research Department, Central Bank of Brazil. E-mail addresses: marcelo.kfoury@bcb.gov.br and sergio.lago@bcb.gov.br 3  ,QWURGXFWLRQ Small-scale macroeconomic models are very useful for forecasting the short run, but they are not very useful for anchoring the key variables in the long run. They are not able to answer questions about the macro equilibrium of the economy, nor to establish fiscal or external constraints. Larger macroeconomic models work better in providing information about the interaction of stabilization and growth in the medium run. Questions concerning technology, investment, labor markets and the current account balance are better addressed by a more comprehensive model. Micro-founded models are also able to present long run properties consistent with economic agents’ optimal behavior. On the other hand Keynesian models are important because they can be used to simultaneously determine the equilibrium levels of output, employment, inflation, current account, rate of investment and fiscal balance. However, in Keynesian models the long-run equilibrium of some key variables such as the interest rate and exchange rate are not endogenously determined. Many Central Banks have built micro founded structural models. Examples include the Bank of Canada’s QPM, the Bank of England’s MM (0DFURHFRQRPLF 0RGHO) and also the IMF’s Multimod. These models are in general divided into two parts. A steady-state part assures long-run equilibrium, which is based on the optimal behavior of economic agents, while a dynamic section describes the equilibrium path of the economy using an error correction framework. The steady-state model of the QPM is an overlapping-generation model with only one good1. The Multimod is very similar and for the first five years uses the outcome from the World Economic Outlook as a baseline. The dynamic section of the Multimod uses a non-linear Phillips curve and also ensures long-run growth consistent with sustainable external debt service. The special features of the FRB-US are the non-arbitrage conditions in the financial markets. In the goods sector, the expectational variables are model consistent. The dynamic model is also based on an error-correction approach. VAR expectations are also taken into account to describe transitory shocks. The steady-state section of the model is not a dynamic general equilibrium model (DGE) but an ad-hoc baseline case. 4 Among the models in the Keynesian paradigm, one example is the Financial Programming model of the International Monetary Fund, which uses the monetarist approach to the balance of payments. This model was used in the creation of an entire generation of IMF programs and is still being applied. The bottom-line is to set a goal for the central bank’s net domestic assets as a way to avoid growth of the money supply well above the floor for international reserves. The World Bank has a line of two-gap growth models (domestic saving and external saving) called RMSM-X. In Brazil, IPEA has set up a Keynesian macroeconomic model, based on the national accounts, especially the balance of payments and the fiscal budget. A quarterly version of this model has been released recently. The Central Bank of Chile has built a Keynesian model very similar to the one presented in this paper. The major difference between the models is in the derivation of the steady-state equilibrium. In the Chilean model, consumption is divided into durable and non-durable goods, which is a future goal for our model. The main contributions of our model, compared to other macroeconomic models developed in the Central Bank of Brazil, are: - Aggregate demand is calculated by estimating: (1) household consumption, investment in (2) machinery and (3) construction, (4) net exports, (5) government spending, (6) government taxes, (7) changes in inventories; - The model uses a Phillips curve that includes dummies for the structural break in the pass-through coefficient in 1999 and a proxy for labor productivity (unit labor cost); - Potential output is estimated by a Cobb-Douglas production function; - The model includes an estimated exchange rate error correction mechanism converging to the Uncovered-Interest-Parity (UIP) equation on the long run, measured in real terms, together with an equation for the risk premium, to which responses for changes in fiscal and external conditions are added;2 - The model includes ad-hoc steady-state conditions for the current account deficit and the primary fiscal surplus. 1 It relies on indirect tax and share of imported consumption to include inflation and the exchange rate in the model. 2 Muinhos, Alves and Riella (2002) have similar equations for UIP and Risk premium. 5 Some simulations for different Taylor rules and impulse responses for a temporary cost-push shock are presented. The paper is organized as follows. Section 2 presents the diagrams of the small macroeconomic and the medium size models, showing the monetary policy transmission mechanisms and presenting some discussion about the long run equilibrium conditions for the external sector. Section 3 presents estimated and calibrated equations for the demand, supply, external and monetary-fiscal blocks of the model. Section 5 shows some simulation exercises and the last section concludes the paper.  'LDJUDPVRI7KH7UDQVPLVVLRQ0HFKDQLVPVDQG(TXLOLEULXP&RQGLWLRQV In order to compare the monetary transmission mechanisms of the medium-scale and the small-scale models, it is necessary to explain the mechanisms in the latter model, as shown in Figure 1. The model includes the traditional channel, via output gap, and a second channel, via exchange rate. The IS curve shows that an increase in the real interest rate will negatively affect the output gap, directly and indirectly via the term structure of interest rates. A more negative output gap will decrease inflation via the Phillips curve. By the UIP non-arbitrage condition, an increase in the interest rate causes an appreciation of the exchange rate in the spot market, and, via the Phillips curve, a decrease in imported prices will generate lower inflation. )LJXUH 6PDOO0RGHO7UDQVPLWLRQ0HFKDQLVP  6 The two monetary transmission mechanisms described for the small model also occur in the medium model, shown in Figure 23. But now it is possible to distinguish between supply and demand effects. An increase in the interest rates will affect household consumption and investment in construction and machinery through the term structure, generating a decrease in aggregate demand. A higher interest rate will cause an exchange rate appreciation and a decrease in net exports, decreasing aggregate demand. On the supply side, the effects of a higher interest rate will take more time to occur, because a lower level of investment will cause a decrease in the growth rate of the capital stock, affecting potential output growth. The decrease in aggregate demand leads to a drop in inflation through a more negative output gap. But this drop would be partially offset by the decrease in potential output growth. The exchange rate mechanism is still available in the medium size model. But now the fiscal and external variables also affect the exchange rate via the risk premium. An increase in the interest rate that worsens the fiscal accounts will generate an increase in the risk premium and a depreciation of the exchange rate that might offset the aggregate demand channel. The current account deficit also affects the risk premium and consequently, the exchange rate and inflation. Rapid GDP growth may cause an increase in inflation via the output gap and also via a worsening of the trade balance. 3 Although the main blocks of the medium model are represented in Figure 2, there are some interactions between variables not shown in the figure in order to obtain a clean representation of the model. Nevertheless, the model equations are commented in the text. As this is still a work in progress, our blocks are subject to future improvements. 7 )LJXUH 0HGLXP0RGHO7UDQVPLWLRQ0HFKDQLVP We also include the labor market as a monetary transmission channel. An increase in the labor force may increase potential output via the Cobb-Douglas production function. In addition, an increase in productivity measured by Total Factor Productivity will increase GDP and decrease inflation, allowing for a loosening of monetary policy. The absence of micro-founded behavior equations does not allow us to find endogenous steady state values for variables such as the interest rate or exchange rate. The exchange rate, for instance, is modeled with an error correction mechanism with UIP as the level relation, driving the system to the long run equilibrium steady-state exchange rate, defined as the exchange rate that leads to an ad-hoc long-run current account/GDP ratio. This ratio, in turn, is consistent with a steady-state ratio of external liabilities/GDP. For the interest rate, the use of the Taylor rule assures a long-run equilibrium compatible with the inflation target and a neutral output gap.  0RGHOLQJWKH%UD]LOLDQ(FRQRP\ The IBGE4 began releasing a quarterly series of the income components of GDP in the third quarter of 2001. The sample starts in 1991:01. This has made it possible to construct and run more detailed macro models for the Brazilian economy. However, 4 Brazilian Institute of Geography and Statistics. 8 studies using these new quarterly data are very recent and the constructed models are still based on a new Keynesian paradigm, using ad hoc relations between the variables rather than micro-founded structural relationships. However, even considering that our results are subject to the Lucas critique in some sense, it is still worth working on the model, due to the fact that it can be used to simultaneously determine the levels of output, employment, inflation, current account, rate of investment and fiscal balance. And it is in line, in some parts, with other models developed using this new Brazilian quarterly data, as in Cavalcanti, Kai and Carvalho (2002). The use of micro-founded models is on our agenda for the next generation of the Central Bank of Brazil’s structural models. The estimation samples depend upon the availability and behavior of the data. We choose not to homogenize the starting point of the estimations. We are estimating each equation separately and if we do not consider the full series we would be throwing information away. Nevertheless when there are severe structural breaks that cannot be fixed with dummy variables, we decide to exclude the series before the break. Inflation before 1994 is a good example of this problem. As we did not estimate the equations in a system, simultaneity bias was avoided using two stage estimations or considering only lagged variables on the right side of the equations.  7KH$JJUHJDWH'HPDQG6LGH Aggregate demand is determined by its definitional identity, shown in Equation 1. In this section, we will model each of its components and related variables such as taxes, government expenditures and the fiscal deficit (primary concept). <W = &W + *W + , W + ; WQHW + ∆6 W :KHUH < RXWSXW & KRXVHKROGFRQVXPSWLRQ * JRYHUQPHQWFRQVXPSWLRQ , LQYHVWPHQW W W W W ; WQHW  QHWH[SRUWV ∆6  W LQYHQWRU\LQYHVWPHQW 9 (1) Although the IBGE releases both nominal and real data, the real income components do not sum to meet Equation 15. As a solution, we estimated real income components using their nominal income share applied to real income. This method guarantees Equation 1, in real terms, for the whole sample.  +RXVHKROG&RQVXPSWLRQ Household consumption is by far the most important income component, since it accounts for more than 60% of output. Although this initial model’s formulation is new Keynesian, the traditional literature strongly indicates that consumption should be a function of permanent rather than contemporaneous income. On the other hand, empirical results suggest that some factors may also cause consumption decisions to be based on contemporaneous income variables. For example, difficulties in obtaining loans and weak forward-looking behavior by some agents may cause this behavior. In this context, we used a very simple specification: a level equation, in logarithms, with the ratio of consumption-to-disposable income on the left side, as shown in Equation 2. In order to capture a permanent income effect, we used potential output6, which we considered a reasonable measure. Contemporaneous income was also tried, but it failed as a regressor7, so we decided to use the real interest rate to capture the same behavior. An increase in the real interest rate should decrease the income growth rate and, in response, the consumption growth rate. Theory indicates that we should consider medium or long-term interest rates rather than short-term interest rates. We could obtain the former considering the 6-month swap market, but this would force us to use a smaller series since we only have 6-month interest rates from 1994Q4 on. Therefore we decided to use the short-term interest rate. Additionally, we used a step dummy variable to capture the increase in the consumption-to-disposable income ratio after 1996, which may have resulted from an improved outlook related to the recent 5 Even when changing base period values in order to guarantee the income identity in some quarters, there are always some periods in which the income identity does not fit. This is probably due to the fact that the individual series are not deflated with the same deflator as the income series. 6 See Section 3.2. 7 We tried a weighted average of permanent and contemporaneous income, with weights to be estimated in the regression, but contemporaneous income was not significant. This is probably due to colinearity between GDP and potential GDP. 10 stabilization of the economy. The outcome of the estimation, which used an outlier pulse dummy for 1994Q18, is shown in Table 1, in. 3 &  &  ln  GW  = α 0 + α1 ⋅ ln  WG−1  + α 2 ⋅ UW −1 + ∑ βL ⋅ 6HDVL + α 3 ⋅ '96 L =1  <W −1   <W −2  (2) :KHUH & KRXVHKROGFRQVXPSWLRQ <W G  GLVSRVDEOHSRWHQWLDOLQFRPH <W 7W G  GLUHFWWD[HV < SRWHQWLDORXWSXW U VKRUW W W W G = <W − 7W G  WHUP π 6HOLF  UDWH U = − 3 π − 4 ∑ 4  =0 UHDO , IURP 199141 WR 199541 W W W W LQWHUHVW , IURP 19954 2 RQ L  L 6HOLFW DQQXDOL]HG%UD]LOLDQRYHUQLJKWQRPLQDOLQWHUHVWUDWH ' VWHSGXPP\IURP\HDURQ 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH -0.308 0.045 -6.873 0.000 0.254 0.123 2.068 0.046 -0.737 0.262 -2.817 0.008 0.060 0.020 2.933 0.006 0.080 0.018 4.559 0.000 0.103 0.017 6.070 0.000 0.055 0.018 3.060 0.004 0.168 0.040 4.172 0.000 R2 = 0.782 R2Ajust. = 0.740 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW α0 α1 α2 β1 β2 β3 α3 D94:01 8 Without the dummy variable, all fitting and residual (serial correlation and heteroskedasticity test) statistics seemed to be acceptable, but we nevertheless observed a huge residual value in 1994Q1 of about 3 times the regression standard error. This could indicate an outlier. Running the regression with a pulse dummy for that period, we find that the new coefficients do not significantly change, but fitting and residual statistics are much better. 9 We considered two measures for the ex-ante real interest rate to correct distortions caused during the hyperinflation period. In post Real Plan period, the 4-quarter inflation average would represent an adaptative ex-ante inflation expectation with 75% (calibrated) backward looking. If this procedure were to be used for the previous period, it would lead to false negative real interest rate, with huge absolute values, from 1994Q3 to 1995Q1. It is due to the fact that the former procedure is incorrect to generate ex-ante interest rate in hyperinflationary periods, during which past values averages systematically underestimate current inflation. 11  ,QYHVWPHQW Like household consumption, investment has an important role in determining economic activity since it affects both output directly, and potential output indirectly via capital accumulation. We break the investment series into its construction and machinery components and model each separately. These two series are best explained by the 6-month real interest rate. Even though the sample size for these series is smaller, as explained in the last section, the regressions seemed to have good explanatory power - good fit and good residual statistics – and we considered them as acceptable representations of reality. Construction and machinery investment are represented in Equations 3 and 4, respectively, and estimation results are shown in Tables 2 and 3, respectively. Total investment is determined by the identity in Equation 5. The behavior of investment seems to have been passed through changes related to the way its components (machinery and construction) were affected by the real interest rate and seasonal movements from 1999 on. Up to 2000Q2, construction investment is affected by 2-lags of the real interest rate; from 2000Q2 forward, it is also affected by 1lag of the real interest rate. With respect to machinery investment, it does not seem to be affected by the real interest rate in 1995. 3  ,&   ,&  6 6ZDS 6 U ' α βL ⋅ 6HDVL + β 4 ⋅ 6HDV1 ⋅ '1999 ln  G W  = α 0 + α1 ⋅ ln  GW −1  + α 2 ⋅ UW 6ZDS + ⋅ ⋅ + ∑ 3 W −1 2000 −2 L =1  <W −1   <W −2  (3) 3  ,0   ,0  6 ln  G W  = $0 + $1 ⋅ ln  GW −1  + $2 ⋅ UW 6ZDS ⋅ '1996 + ∑ %L ⋅ 6HDVL + %4 ⋅ 6HDV2 ⋅ '1999 −1 L =1  <W −1   <W − 2  (4) , = ,& + ,0 (5) W W W :KHUH , WRWDOLQYHVWPHQW W ,&  FRQVWUXFWLRQLQYHVWPHQW ,0  PDFKLQHU\LQYHVWPHQW <  UHDOLQFRPH W W W UW 6ZDS   PHGLXP UXQ UHDO , XQWLO 199541 π LW6ZDS 6  3  = −  π W −L IURP 4 RQ , 1995 2 4 ∑   L=0 4 W UW 6ZDS 6 LQWHUHVW  12 UDWH LW6ZDS   DQQXDOL]HGPRQWKVZDSLQWHUHVWUDWH '\\\\ VWHSGXPP\IRU\HDU³\\\\´RQ 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH -1.393 0.312 -4.466 0.000 0.336 0.159 2.112 0.047 -1.010 0.502 -2.011 0.057 -2.300 0.629 -3.658 0.001 0.097 0.034 2.806 0.011 0.161 0.019 8.554 0.000 0.124 0.020 6.351 0.000 0.073 0.029 2.524 0.020 R2 = 0.831 R2Ajust. = 0.775 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW α0 α1 α2 α3 β1 β2 β3 β4 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH -1.458 0.309 -4.716 0.000 0.497 0.120 4.142 0.000 -1.625 0.717 -2.265 0.033 0.171 0.023 7.568 0.000 0.212 0.025 8.562 0.000 0.119 0.021 5.600 0.000 -0.065 0.028 -2.303 0.031 R2 = 0.902 R2Ajust. = 0.877 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW Α0 Α1 Α2 Β1 Β2 Β3 Β4  1HW([SRUWV Since nominal exports and imports, in US dollars, are modeled in Sections 3.3.3 and 3.3.4, modeling real exports and imports is quite simple. We only have to transform the currency into Brazilian real and deflate the series, as described in Equations 6 and 7. Net exports are determined by the definition in Equation 8. ∆ OQ(; ) = ∆ OQ(([SRUWV ) − ∆H − π W OQ(0 W W )= W OQ(,P SRUWV ) − H − W ; WQHW = ; W− 0 W   13 W (6) W W (7) (8) :KHUH ([SRUWV  QRPLQDO86GROODUH[SRUWV W ,PSRUWV  QRPLQDO86GROODULPSRUWV W H H[FKDQJHUDWH ORJDULWKP  W π W  ,3&$LQIODWLRQUDWH  *RYHUQPHQW&RQVXPSWLRQ Brazil’s fiscal surplus (primary concept) is defined as total tax revenues minus non-interest government expenditures. The former are divided, as usual, into direct and indirect taxes and the latter are divided into government investment and government consumption. We model total taxes as a function of lagged total taxes and lagged income in a simple specification described in Equation 9. In order to capture the most recent behavior of tax policy, the estimation sample was very short; the result is shown in Table 4. A step dummy was used to model a level change that occurred from 1999 on and a pulse dummy was used to capture a 1997:04 outlier. Direct taxes, modeled in order to have a measure of disposable income (<W − 7W G ), are modeled by a similar specification, described in Equation 10. Its output is shown in Table 5. Government investment, as a ratio of total taxes, is modeled as a AR(3) process described in Equation 11, with outlier dummies. The result is shown in Table 6. Government consumption is calculated as a residual, in Equation 12, since we determined an exogenous path for the fiscal deficit (primary concept) as a GDP ratio (annual average). 3 7W7 = α 0 + α 1 ⋅ 7W7−1 + ∑ β L ⋅ <W −L (9) L =1  7W G = α  + α  ⋅ 7W −G + ∑ β L ⋅ <W −L (10) , W* , W*−1 , W*−2 , W*−3 α α α α = + ⋅ + ⋅ + ⋅ 0 1 2 3 7W7 7W7−1 7W7−2 7W7−3 (11) L = 3 ( ) 3 3 M =0 M =1 *W = ∑ 7W7− M − )635W ⋅ ∑ <W − M − ∑ *W − M M =0 :KHUH 7W7  WRWDOWD[ 7W G  GLUHFWWD[ , W*  JRYHUQPHQWLQYHVWPHQW 14 (12) )635  W ILVFDOGHILFLW SULPDU\FRQFHSW  7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH -25.297 12.177 -2.077 0.053 -0.391 0.097 -4.050 0.001 0.464 0.079 5.889 0.000 -0.290 0.083 -3.475 0.003 0.371 0.079 4.697 0.000 -4.782 1.004 -4.762 0.000 -10.449 1.684 -6.205 0.000 R2 = 0.926 R2Ajust. = 0.899 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW α0 α1 β1 β2 β3 D99 D97:04 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR &RHIILFLHQW (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH α0 -29.538 11.458 -2.578 0.020 α1 -0.449 0.104 -4.333 0.000 β1 0.342 0.075 4.546 0.000 β2 -0.231 0.083 -2.779 0.013 β3 0.288 0.078 3.675 0.002 D99 4.224 1.000 4.226 0.001 D97:04 -9.587 1.674 -5.726 0.000 R2 = 0.899 R2Ajust. = 0.863 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   7DEOH (TXDWLRQ 0HWKRG 2/6 :KLWH+HWHURVNHGDVWLFLW\&RQVLVWHQW6WDQGDUG(UURUV &RYDULDQFH 6DPSOH WR &RHIILFLHQW (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH α0 0.031 0.012 2.497 0.022 α1 0.509 0.142 3.584 0.002 α2 0.447 0.173 2.581 0.019 α3 -0.320 0.171 -1.871 0.078 D96:02 0.032 0.003 9.171 0.000 D97:04 0.072 0.002 31.423 0.000 R2 = 0.859 R2Ajust. = 0.820 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S    ,QYHQWRU\,QYHVWPHQW We define the inventory dynamics as follows: 6 = (1 − δ )⋅ 6 −1 + ∆6 −1 W W  15 W (13) :KHUH 6 LQYHQWRU\OHYHO W ∆6  LQYHQWRU\LQYHVWPHQW δ GHSUHFLDWLRQUDWHLQYDULDQWRYHUWLPH W The basic hypothesis is that firms produce in order to maintain a minimum inventory as a long run time invariant demand ratio 6 , where Zt = Yt - ∆St. Keeping = this assumption in mind and dividing both sides of Equation 13 by Zt , we obtain the result described in Equation 14, considering that =W +1 = =W ⋅ (1 + JW=+1 ) . In the steady state, the ratio equilibrium ratio 6 should converge. Hence, in Equation 15, = ∆6 depends on the depreciation rate plus the quarterly Z growth. 6 6W +1 6W 6 6 ∆6 − = − JW=+1 ⋅ W +1 − δ ⋅ W + W =W +1 =W =W +1 =W = W (δ + J W= )⋅ =6W +1 W = ∆6 W =W ∴ ∆6 W = δ + J W=+1 6W ( (14) ) :KHUH =W +1 = =W ⋅ (1 + JW=+1 )  J W=  TXDUWHUO\= JURZWKUDWH W Assuming that the inventory dynamics over the last decade (1991/2001) have behaved on average as indicated by Equation 15, we can estimate two latent variables related to inventory formation: the initial inventory (1991:01) and the depreciation rate (δ). Note that if the ratio ∆6 is supposed to be constant over the sample, the sum of the 6 quadratic deviations from the sample average must be minimized. In this context, we just have to find the values of those two non-observed variables that minimize the previous sum, since the values of J W=+1 are known. Doing this we find 6  and δ  DQQXDOEDVLV   16 (15) (VWLPDWLQJD'\QDPLF,QYHQWRU\,QYHVWPHQW0RGHO A deviation of inventory investment from the long run relationship means that the economy is growing faster or slower than expected, should inventory investment be below or above the long run relationship, respectively10. Consider the case, for example, when the growth of demand is slower than expected. Since firms, on the other side, have already decided to produce in order to achieve the expected demand plus the long run inventory investment, there must be a positive gap between actual and long run ∆6 6 ratio. What happens next? Firms decide to produce less, running in the opposite direction, correcting the gap until it is closed again. This may produce an over shooting ∆6 gap, as has been observed in the Brazilian inventory 6 dynamic behavior for the investment series. On the other hand, production decisions may also be negatively affected by the real interest rate. Hence, we model the ∆6 gap as a function of it own lags and of the real interest 6 W W ∆6 is modeled with the potential Zt growth rate, considering that it 6 must equal the potential output growth rate in the long run, as shown in Equation 16. Table 7 shows the estimations, which include a dummy to reflect a reduction in the level that occurred from 1994Q1 to 1997Q4. W rate. Potential W JW = ∑ α L ⋅ JW −L + α 4 ⋅ (UW −3 − U HT ) 3 (16) L =1 :KHUH J W LQYHQWRU\LQYHVWPHQWUDWLRJDSGHILQHGDV J W =  <  ∆6  − δ +  − 1   6  < −1    W W < SRWHQWLDORXWSXW U HT  VKRUWUXQHTXLOLEULXPUHDOLQWHUHVWUDWH W 10 W W Indeed, it can be used as a leading indicator for the output gap, due to the cited reasons. 17 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH -0.930 0.126 -7.377 0.000 -0.793 0.139 -5.685 0.000 -0.622 0.117 -5.320 0.000 -0.431 0.221 -1.947 0.059 -0.052 0.014 -3.691 0.001 R2 = 0.646 R2Ajust. = 0.597 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW α1 α2 α3 α4 D9497  7KH6XSSO\6LGH The supply side was modeled using a traditional Cobb-Douglas production function approach and a Phillips type curve. &REE'RXJODV3URGXFWLRQ)XQFWLRQ A Cobb-Douglas production function, with capital and labor, was modeled as described in Equation 17. < = $ ⋅ (. ⋅ XFL W W W W )α ⋅ (/ )1−α W W W :KHUH / = 3($ ⋅ (1 − X W W . = (1 − δ )⋅ . W W ) 4 W −1 + ∑ β ⋅ , L L 4 ∑β L =2 L =2 W −L  =1 3($ ODERUIRUFH $JH≥\HDUV  X XQHPSOR\PHQWUDWH   XFL LQVWDOOHGLQGXVWULDOFDSDFLW\XVHG   δ GHSUHFLDWLRQUDWH 11 Released on a monthly basis by the %UD]LOLDQ ,QVWLWXWH RI *HRJUDSK\ DQG 6WDWLVWLFV (IBGE), the 3RSXODomR(FRQRPLFDPHQWH$WLYD (PEA) is the potential labor force in the economy, accounting for employed people and unemployed who looked for a job in the last 30 days, both older than 15 years. 12 Released on a monthly basis by the %UD]LOLDQ,QVWLWXWHRI*HRJUDSK\DQG6WDWLVWLFV (IBGE). 13 Released on a quarterly basis by the %UD]LOLDQ)XQGDomR*HW~OLR9DUJDV (FGV). 14 We considered, for simplification sake, that capital inventory depreciates by the same rate estimated in the inventory investment section. 18 (17) The total factor productivity (TPF) series is extracted as a residual of Equation 17, since the GDP, PEA, u, uci and αW series are known. It is important to emphasize here that the TPF series (At) depend only on the latent values of βL and on the initial capital inventory (.). Knowing the TPF series, we can define potential output as in Equation < 18. The output gap15, written in a logarithmic form K = ln < W W W   , can be easily derived  as described in Equation 1916. ( ) <W = $W ⋅ (. W ⋅ XFL IH ) ⋅ /WIH α [ W 1−α W (18) ] KW = α W ⋅ ln (XFLW ) − ln (XFL SH ) + (1 − α W )⋅ [ln (1 − X W ) − ln (1 − X )] :KHUH /WIH = 3($W ⋅ (1 − X ) X QDWXUDOXQHPSOR\PHQWUDWH   IH IXOOHPSOR\PHQWLQGH[ Note that each quarter’s investment contributes to capital formation up to 4 quarters ahead. The intuition behind this modeling is that certain investments may be converted into capital faster than others. However, we restricted the investment percentage lag to be between 2 and 4 quarters. In this model, we use a dynamic behavior for α, the capital share yield. Actually this series had a structural break in 1994 as shown in Graph 1, which plots annual values17. In order to obtain α quarterly values, we considered an alternative procedure that assured a smooth pattern and annual quarterly values average restriction, as described and justified in Appendix 1. A visual comparison between annual and quarterly estimated values is presented in Graph 2. Due to the fact that the IBGE has only released data up to 2000, we used α forecasts simulated by Equation 26 in order to estimate the output gap and potential output through 2001. 15 16 “Hiato” in Portuguese. Note that output gap can be view as a weighted average of the utility capacity gap and the employment rate gap. However, in the simulations, we did not model X and XFL . Hence, the simulations of the W W output gap are obtained from aggregate demand, output and the potential output described here. 17 Released on a annual basis by the %UD]LOLDQ,QVWLWXWHRI*HRJUDSK\DQG6WDWLVWLFV (IBGE) on “Table 4 Composição do Produto Interno Bruto sob as três óticas - 1996-2000”, Contas Nacionais do Brasil. 19 (19) In the following, we will present some results based on Solow’s growth model considering the effect of a volatile path for α. First, we rewrite the potential output equation considering labor efficiency (Et), as in Equation 21. Equation 22 shows the last equation transformed into a logarithm first difference. It is a well-known result that, in steady state, N W IH and ( should grow at the same rate. Accepting that the first W difference in the natural logarithm equals the growth rate, we may expect that in the steady state or in a sufficiently large sample, Equation 22 converts to Equation 2318. *UDSK6WUXFWXUDOEUHDNRIFDSLWDOVKDUH\LHOG ( ) ⋅ (( ) \W = N W IH α 1−α W W ( ) ( ) ∆ ln(\W ) = α W ⋅ ∆ ln NW IH + ln NW IH−1 ⋅ ∆(α W ) + (1 − α W )⋅ ∆ ln((W ) − ln((W −1 )⋅ ∆(α W ) ] ∆ ln(\W ) = ∆ ln N W IH + ln N W IH−1 − ln((W −1 ) ⋅ ∆(α W ) :KHUH 1 (W = ( $W )1−α \W = W <W /WIH NW IH = .W ⋅ XFL IH  /WIH Regarding Equation 23, where both sides are functions of non-observed variables (., βL, XFLIH and X )19, its empirical validation depends heavily upon the estimates – or calibrations – of those latent variables. Hence, we decided that the estimation of these variables should include an optimization process aimed at reducing the deviations between both sides, over a sample in which we could validate the main hypothesis of this result, namely that N W IH and ( grow by approximately the same rate. There was W 18 A particular case is when αt is time invariant, the second term on the right side vanishes and we obtain the known result that 19 N W IH and \ grow by the same rate as well as ( . W W Remember that δ is already estimated. 20 2000.I (21) W ( ) [( ) 1999.I 1998.I 1997.I 1996.I 1995.I 1994.I 2000 1993.I 0.45 1992.I 0.45 W 1991.I 0.48 *UDSK4XDUWHUO\D VHULHV 1990.I 0.48 1999 0.50 1998 0.50 1997 0.53 1996 0.53 1995 0.55 1994 0.55 1993 0.58 1992 0.58 1991 0.60 1990 0.60 (22) (23) another restriction that should be considered here. However, it is a restriction present in the Phillips curve modeled in the next section. After modeling this curve, we will present the latent variables estimation process.  3KLOOLSV&XUYH0RGHOLQJ A Phillips curve, as usual, should consider an expected inflation rate, a measure of the level of activity such as the output gap, and also a pass-through component, to capture changes in import prices. Concerning this last component, we model a structural break in the pass-through coefficient after the move to a floating exchange rate regime in January 1999. We assume that, under the new regime, movements in exchange rates will not be perceived to be as permanent as they were in the crawling peg regime. Thus, expecting this coefficient to be smaller under the floating exchange rate regime, we introduced a step dummy in a non-linear pass-through coefficient in order to capture the structural break. With respect to inflation expectations, we should make some remarks concerning administrative prices. In Brazil, administrative prices have a high weight in the IPCA20 basket, averaging around 30% of the total index. Forecasting these prices is more accurate one year ahead, mainly because of the readjustment clauses contained in the contracts governing these prices. In this context, our Phillips curve models just the "free prices"21, which should respond to monetary policy22. But free price inflation expectations must be a function of full inflation, with backward and forward components. A final feature of the specification is a verticality long run restriction: there must be no intercept coefficient, and backward and forward coefficients and the passthrough coefficient must sum to 1. The absence of an intercept coefficient is the final restriction to be used on the latent variables estimation mentioned earlier. This restriction should be considered in the estimation described in the next section. Attempting to capture all those features, the Phillips curve specification is given in Equation 2423. 20 Measured and released on a monthly basis by the Brazilian Institute of Geography and Statistics (IBGE), IPCA is the consumer price index chosen for the purpose of gauging yearly inflation targets in the Inflation Target system. 21 Purging government prices. 22 In our simulations, we considered the government inflation forecasts up to one year ahead based on the contracts. But, for longer forecasting horizons, we assume that government prices should move together with free prices. 23 The Phillips curve estimation output will be shown in Table 8 Section 3.2.3. 21 W IUHH = 1 ⋅ W −1 + (1 − 1 − 3 − 4 ⋅ ' IO )⋅ (W W +1 + 2 ⋅ KW −1 + ( 3 + 4 ⋅ ' IO )⋅ ( HW + W ) :KHUHDOOYDULDEOHVDUHVSHFLILHGLQORJDULWKPV π W IUHH  IUHHLQIODWLRQUDWHFRQVLGHULQJWKH,3&$ π IXOOLQIODWLRQUDWHFRQVLGHULQJWKH,3&$  W π * IRUHLJQLQIODWLRQUDWHFRQVLGHULQJWKH8633, K  RXWSXWJDS KLDWRLQ3RUWXJXHVH  H  H[FKDQJHUDWH '  VWHSGXPP\EHIRUHH[FKDQJHUDWHUHJLPHFKDQJLQJDQGDIWHU W W W IO  (VWLPDWLRQRI1RQ2EVHUYHG9DULDEOHV As commented in Boone, Juillard, Laxton and N’Diaye (2002), NAIRU estimation processes that do not exploit information about inflation may result in inefficient historical measures of the NAIRU, biased parameter estimates, as well as inefficient forecasts of the NAIRU. In this work, rather than taking into account the path of the NAIRU, we assumed a constant natural rate of unemployment. Nevertheless, as this last critique suggests, we must use inflation information to estimate the latent variables. In this sense, we considered a Phillips curve restriction described as follows: As previously mentioned, the latent variables estimation process must approximate both sides of Equation 23, over a sample in which we could validate the main hypothesis of this result, meaning that N W IH should converge. On the other hand, Equation 24 should have no intercept. We assume here that the only reason why the Phillips curve should have a significant intercept is from a misestimated output gap. Hence, in each interaction of the estimation process, there are two phases: the first consists of a optimization process in which we estimate the latent variables in order to minimize the quadratic sum of the difference between both sides of Equation 23, as described in System 25. The sample used in the optimization process is from 1995:1 to 2001:4, because in this period N W IH seemed to be very stable. 22 (24) min  ∑ W { ln(\ )− [ ln(N )+ [ln(N )− ln(( )]⋅ ( )]} IH W IH W −1 W 2 W −1 W (25) 6XEMHFW WR 0≤ L XFL IH DQG X ≤ 1 The second phase of each interaction consists of estimating Equation 24 with an intercept. Assuming that the only misestimated variable is the output gap generated in the first phase, and assuming that this error should be related to the XFLHI , the intercept value should be equal to α 2 ⋅ ε K ⋅ α , where ε K ⋅ α is the XFLHI error multiplied by average αW. Therefore, we could estimate the XFLHI error, and a new measure of XFLHI . With the new XFLHI estimated, we could run phase one again but with the restriction that XFLHI should be equal to theestimated value. The process generates another value for the natural rate of unemployment that should be consistent with the imposed XFLHI. With new estimates, we could do phase 2 again restarting the cycle of interactions. It is important to note that, in each second phase, the intercept got less and less significant. With the estimated parameters, we could estimate24 Equation 24 without an intercept term, but including two outlier dummies, as shown in Table 8. In convergence, the process estimated: . 0 = 904.25 XFL IH = 84.93% X = 5.29% β 4 = 0 β 3 = 0 β 2 = 1 7DEOH (TXDWLRQ 0HWKRG 76/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH 0.212 0.122 1.743 0.096 0.311 0.062 5.009 0.000 0.510 0.148 3.452 0.002 -0.453 0.149 -3.046 0.006 0.026 0.009 2.927 0.008 0.018 0.008 2.079 0.050 R2 = 0.809 R2Ajust. = 0.763 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV 1⋅5  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW α1 α2 α3 α4 α99:04 α00:03 24 This equation was estimated using Two-Stage Least Squares with lagged inflation and inflation forecasts made by a univariated model, as instrumental variables for the forward component. The results are robust and we could confirm that pass-through coefficient reduced from about 51% to 6% after changing the exchange rate regime. 23  0RGHOLQJWKH&RPSRQHQWVRIWKH&REE'RXJODV3URGXFWLRQ)XQFWLRQ Regarding the fact that there was no prior information about the future dynamics of αt, we simply estimated an ARIMA (3;1;0) model with no intercept in order to avoid a non-justified trend, as shown in Equation 26. The estimation outcome is described in Table 9. The total factor productivity (At) was modeled, in logarithm, by a seasonal ARIMA (2;1;0), as shown in Equation 27 and its estimation outcome is described in Table 10. PEA was modeled in logarithms with an autoregressive component, linear trend and seasonality. In an effort to account for a level change that occurred after 1994:3, we introduced a step dummy. The specification is shown in Equation 28 and the estimation outcome is described in Table 11. And, finally, the capital inventory, obtained by the estimated parameters into its definition in Equation 5, is shown in Equation 29. ∆α = β 1 ⋅ ∆α W W + β 2 ⋅ ∆α −1 W + β 3 ⋅ ∆α −2 W (26) −3 3 ∆ ln ($ ) = β 0 + β 1 ⋅ ∆ ln ($ −1 ) + β 2 ⋅ ∆ ln ($ − 2 ) + ∑ α ⋅ 6HDV W W W L L L (27) =1 3 ln (3($ ) = β 0 + β 1 ⋅ ln (3($ −1 ) + β 2 ⋅ 7UHQG 91:01 + ∑ α ⋅ 6HDV + β 3 ⋅ '94:03 W W L L . = 0.98 ⋅ . W 7DEOH W −1 +, W L −2 (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH 2.200 0.117 18.784 0.000 -1.926 0.176 -10.930 0.000 0.619 0.090 6.851 0.000 R2 = 0.985 R2Ajust. = 0.983 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW β1 β2 β3     24 (28) =1 (29) 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH -0.052 0.012 -4.294 0.000 0.745 0.182 4.082 0.000 -0.380 0.148 -2.568 0.017 0.083 0.020 4.160 0.000 0.080 0.017 4.626 0.000 0.056 0.017 3.316 0.003 R2 = 0.673 R2Ajust. = 0.602 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW β0 β1 β2 α1 α2 α3 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH WR (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH 6.2527 1.805 3.464 0.001 0.6225 0.109 5.710 0.000 0.0014 0.000 2.947 0.006 -0.0058 0.003 -2.017 0.051 0.0041 0.003 1.434 0.160 0.0027 0.003 0.979 0.334 0.0090 0.004 2.470 0.018 R2 = 0.987 R2Ajust. = 0.985 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S   &RHIILFLHQW β0 β1 β2 α1 α2 α3 β3  ([WHUQDO%ORFN The exchange rate and sovereign risk premium are modeled in the next two subsections on a monthly basis in order to capture their movements more precisely. In quarterly analysis, important information may be lost. In that case, it is important to reestimate quarterly coefficients in order to keep the same impulse response features, which are not guaranteed when we consider the same autoregressive and error correction coefficients in the monthly and quarterly specifications. The procedure is very simple. Long run coefficients, excluding those that are autoregressive, should be the same in both frequencies, and convergence velocities must be the same as well. If in the monthly specification the autoregressive coefficient is 0.7, for instance, it should be (0.7)^3 in the quarterly specification. Another example is the error correction term. If in the monthly specification it takes 9 months to achieve halflife, for instance, it should take 3 quarters in the quarterly specification. 25 When it is not that easy to derive quarterly coefficients, we recommend a optimization procedure, in which the coefficients are chosen in order to minimize a fitting function25 between the quarterly average of monthly values of the original impulse response and quarterly values of the quarterly impulse response, generated by the coefficients to be determined.  ([FKDQJH5DWH We modeled the exchange rate with an equation based on a UIP non-arbitrage condition. As described completely in Muinhos, Alves and Riella (2002)26, there is a strong short run first difference relationship between the Brazilian exchange rate, CBond spread over treasury27 and interest rate differential, all in nominal vales28. But, surprisingly, despite the fact that all coefficients are significant and have the expected sign, they are all greater than unity, in absolute values, as predicted by UIP, even when correcting for the sovereign risk premium. This may be a result of frictions and assymetric information. Nevertheless, the UIP condition should prevail in the long run. With this in mind, we carry out an error correction model for the first difference of the real exchange rate , capturing the short and long run dynamics. The long run and the error correction first difference specifications are described in Equation 30a and 30b, respectively. Their outcome estimations are shown in Table 12a and 12b, respectively. We observed that, in the long run level specification; permanent shocks to the risk premium produce an over-shooting behavior, since there is a strong contemporaneous response that then decreases after one period. It is interesting to note that the permanent coefficient is very close to the 1, as predicted by UIP. As reported in the empirical literature, the real interest rate differential is not significant, but has the correct sign. As 25 Absolute errors sum, squared errors sum, fourth power errors sum, and so on, depending on the influence of smaller errors is intending to affect the fitting function. 26 In this paper, we comment about the UIP puzzle, the literature about exchange rate, and some results cited here. 27 The authors found out that C-Bond spread over treasury should embody the information of the Brazilian sovereign risk and should be free of exchange rate risk, as justified in the cited paper. 28 A first difference logarithm equation is the left-hand side variable, because the authors could not reject the null hypothesis that exchange rate has a unit root in the used sample. The exchange rate expectation was modeled as a lagged exchange rate plus the expected inflation differential, in order to maintain the real exchange rate constant. The risk premium was modeled as a linear function of the CBond spread over treasury. And, instead of imposing a unitary interest rate differential coefficient, with negative signal, they dropped this arbitrage condition and estimated the coefficients. 26 a solution, we imposed a UIP predicted coefficient equal to -1. Regarding the expectation term, we considered an adaptative weighted average with a backwardlooking component, a forward-looking component and a long run equilibrium real exchange rate. The latter is calibrated as the real exchange rate necessary to achieve an ad hoc current account surplus in the long run in each simulation. The short run specification, in first difference, is purely backward looking, but no theory coefficient was imposed. It is interesting to note that real exchange rate changes are affected by the change of one-lagged real interest rate differential instead of the contemporaneous differential. All coefficients were significant and with the correct sign, but as in Muinhos, Alves and Riella (2002), much greater than the129 as predicted by UIP. And the error correction term is slightly greater than one, indicating an overshooting returning to the equilibrium, with a vanishing oscillatory behavior, which confirms empirical evidence in Brazil. Note that those coefficients represent monthly behavior, which is more volatile than the quarterly behavior. When quarterly coefficients are calculated by the procedure described previously, this volatility is smoothed. We also added two dummy variables in order to capture outliers. ε W =  − α  − α  ⋅ ε HT + α  ⋅ ε W − + α  ⋅ (W ε W + − (UW − UW I )+ α  ⋅ 6&%RQGW + α  ⋅ 6&%RQGW − + µ ∆ε W = $ ⋅ ∆ε W − + $ ⋅ ∆ (UW − − UW −I  )+ $ ⋅ ∆6&%RQG W + $ ⋅ µ W − :KHUHDOOYDULDEOHVDUHVSHFLILHGLQORJDULWKPV ε W  UHDOH[FKDQJHUDWH ε HT  HTXLOLEULXPUHDOH[FKDQJHUDWH U VKRUWUXQUHDOLQWHUHVWUDWH UW W I = 6HOLFW  W,3&$ − ∑ −   L =  IRUHLJQVKRUWUXQUHDOLQWHUHVWUDWH UW U  W 6&%RQG  &%RQGVSUHDGRYHUWUHDVXU\ W µ 29 W  HUURUWHUPVXSSRVHGWREHUDQGRP In absolute values. 27 I = )HG)XQGVW  W33, − ∑ −L   L =  W (30a) (30b) 0HWKRG 76/6 W −L 7DEOHD (TXDWLRQD 6DPSOH 0DUWR6HS ,QVWUXPHQWV L = 1WR12 U −1 − U −1 6&%RQG I W &RHIILFLHQW α α α α (VWLP9DOXH 0.692 0.278 20.559 -19.620    W 6W'HYLDWLRQ 0.072 0.073 7.097 7.085 W −L L = 1WR12 7 9.578 3.811 2.897 -2.769 39DOXH 0.000 0.000 0.006 0.009 R2 = 0.978 R2Ajust. = 0.976 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV 2EV 5VTXDUHG  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW2EV 5VTXDUHG  S   0HWKRG 76/6 W − ( ) 7DEOHE (TXDWLRQE 6DPSOH $SUWR2FW ,QVWUXPHQWV  UW − − UW −I  6&%RQG W −L L = WR  &RHIILFLHQW $ $ $ $ ' '        (VWLP9DOXH 0.826 -3.900 16.384 -1.317 -0.058 -0.058 W − &XU$FF*'3W −L L = WR 6W'HYLDWLRQ 0.134 2.015 7.016 0.281 0.020 0.021 7 6.171 -1.936 2.335 -4.683 -2.892 -2.812 39DOXH 0.000 0.061 0.025 0.000 0.006 0.008 R2 = 0.859 R2Ajust. = 0.840 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S    5LVN3UHPLXP We modeled C-Bond spread over treasury, used in Equations 30 and 31, in order to capture sovereign risk perceptions generated by fiscal variables, external trade and solvency/liquidity variables.30 The downward trend in the C-bond yield curve as it gets closer to its maturity was not considered in the simulations. Using a parsimonious criterion, we focused on relevant variables and avoided over fittingestimations. In the best-fit estimation, foreign reserves (%GDP), public debt (%GDP) and current account balance (%GDP) coefficients were significant and representative of fiscal variables, external trade and solvency/liquidity indicators 31 . The specification is described in Equation 31 and its output estimation, by TSLS, is shown in Table 13. 30 31 For a detailed description of the treatment on the risk premium see Muinhos, Alves and Riella (2002), Defying intuition, exchange rate volatility did not have significant explanatory power for the risk premium. 28 6&%RQG = α 0 + α 1 ⋅ 6&%RQG −1 + α 2 ⋅ ∆ Re V / *'3 + W W W (31) + α 3 ⋅ ∆3' / *'3 + α 4 ⋅ &XU$F / *'3 W W :KHUH 5HV*'3  IRUHLJQUHVHUYHV *'3 3'*'3  SXEOLFGHEW *'3 W PRQWK PRQWK W   &XU$F*'3 PRQWKDFFXPXODWHGFXUUHQWDFFRXQWEDODQFH *'3 PRQWK W  7DEOH (TXDWLRQ 6DPSOH -DQWR'HF ,QVWUXPHQWV 6&%RQG W −  5H V3,%W  5H V3,%W  ∆'/73,%W 7&RU3,%W H HW −  0HWKRG 76/6 &RHIILFLHQW α0 α1 α2 α3 α4 (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH -0.0004 0.0044 -0.0821 0.9348 0.8597 0.0472 18.2134 0.0000 -0.8396 0.4274 -1.9646 0.0536 0.1360 0.0788 1.7259 0.0890 -0.2536 0.1074 -2.3608 0.0212 R2 = 0.874 R2Ajust. = 0.867 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   White Heteroskedasticity Test: F = 0.910 (p =0.543)  ([SRUWV In this section and in the next, we present our nominal net export modeling in US dollars. For simplification sake, we modeled export and import quantities. Prices are modeled as ARMA processes, as described in Muinhos, Alves and Riella (2002). Equation 32 presents the quarterly estimates for the export quantity index. The sample starts in 1988 and the coefficients and the t statistics are in Table 14. In the literature there are some papers that also estimate the price (real exchange rate) and income (world GDP) elasticities for exports. Pastore e Pinotti (1999) e Gonzaga e Bevilacqua (1997) found similar coefficients for the income elasticity. However the price elasticity of 0.14 was smaller than found for those papers. Pastore e Pinnoti (1999) for example estimated at 0.24 for the price elasticity and 0.81 for the world income elasticity. 3 exp = α 0 + α1 ⋅ exp −1 + α 2 ⋅ \ * + α 3 ⋅θ −1 + α 4 ⋅ OS[W + ∑ β ⋅ 6HDV + W W W W W M + α 5 ⋅ '91:03  29 =1 M M (32) :KHUH H[S \ TXDQWLWDWLYHLQGH[RIH[SRUWVIRUSHULRGW W  ZRUOG*'3IRUSHULRGWPHDVXUHGDVWKHORJRIWKHZRUOGLPSRUWV W  θ UHDOH[FKDQJHUDWHIRUSHULRGW W OS[W  SULFHLQGH[RIH[SRUWVIRUSHULRGW 6HDV VHDVRQDOGXPPLHV W M '   RXWOLHUGXPP\IRU 7DEOH (TXDWLRQ 0HWKRG 2/6 &RHIILFLHQW (VWLP9DOXH 6W'HYLDWLRQ α0 -0.572 0.804 α1 0.559 0.081 α2 0.445 0.085 α3 0.139 0.054 α4 -0.257 0.137 β1 -0.090 0.024 β2 0.151 0.026 β3 0.098 0.022 α5 -0.239 0.056 6DPSOH 1988:01 to 2001:02 7 39DOXH -0.711 0.481 6.865 0.000 5.249 0.000 2.561 0.014 -1.874 0.067 -3.729 0.001 5.822 0.000 4.554 0.000 -4.307 0.000 R2 = 0.954 R2Ajust. = 0.946 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S    ,PSRUWV Equation 33 presents the estimations of the import quantity index, with coefficients and t statistic value shown in Table 15. The quantity index for imports presents a structural break in the first half of nineties, which makes it necessary to introduce a level dummy in order to avoid a unit root process. Our coefficient for the real exchange rate is smaller that the one usually seen in the literature. However the income-elasticity is closer to other estimations. Pastore e Pinotti (1999) found the price-elasticity of (-0,96) and their income elasticity is 1,02 (taking into account industrial production). Even considering a level dummy after 1993, it seems that the income elasticity still presents a structural break after that year. When we shrink the sample, this coefficient almost doubles. 3 LPS W = α 0 + α 1 ⋅ LPS W −1 + α 2 ⋅ \ W + α 3 ⋅ θ W −1 + ∑ β M ⋅ 6HDV M + M =1 + α 4 ⋅ 'LPS + ∑ β DD:WW ⋅ 'DD:WW DD:WW 30 (33) :KHUH LPS W \ TXDQWLWDWLYHLQGH[IRULPSRUWVLQSHULRGW GRPHVWLF*'3LQSHULRGW W θ UHDOH[FKDQJHUDWHLQSHULRGW W 6HDV VHDVRQDOGXPPLHVIRUWKHSHULRGM 'LPS VWHSGXPP\WKDWLVXQWLODQGDIWHUEHLQJLQEHWZHHQ 'DDWW RXWOLHUGXPPLHVIRUDQG M 7DEOH (TXDWLRQ 0HWKRG 2/6 &RHIILFLHQW (VWLP9DOXH 6W'HYLDWLRQ 6DPSOH WR 7 39DOXH α0 -3.077 1.610 -1.911 0.063 α1 0.568 0.081 7.039 0.000 α2 1.170 0.413 2.831 0.007 α3 -0.191 0.082 -2.337 0.024 β1 -0.102 0.038 -2.675 0.011 β2 -0.016 0.036 -0.442 0.661 β3 0.024 0.040 0.595 0.555 'imp 0.332 0.099 3.367 0.002 '95:03 -0.189 0.094 -2.004 0.051 '97:01 -0.305 0.090 -3.382 0.002 '99:01 -0.206 0.089 -2.302 0.026 R2 = 0.985 R2Ajust. = 0.982 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S    )RUHLJQ'LUHFW,QYHVWPHQW Equation 34 presents the estimated equation for Foreign Direct Investment, with outcomes shown in Table 16. The presence of profit and the first difference of the risk premium in the FDI equation are important, not only in terms of significance but also with expected sign. An increase in the risk premium is a leading indicator of a decrease in FDI, while an increase in profit remittances is an indicator of an increase in FDI. )', = α 0 + α 1 ⋅ )', W W −1 + α 2 ⋅ ∆( 6&%RQG −1 ) + α 3 ⋅ \ −1 + α 4 ⋅ OXFUR −1 W W :KHUH: FDIt Foreign Direct Investment in period t , in 2000 US$; ∆(SCBondt) first difference in the spread of C-Bond in period t; 31 W (34) yt GDP in period t; lucrot net profit in the Balance of Payment in period t, is 2000 US$. 7DEOH (TXDWLRQ 0HWKRG: 2/6 6DPSOH: WR &RHIILFLHQW (VWLP9DOXH 6W'HYLDWLRQ 7 39DOXH α0 -18.840 8.663 -2.175 0.041 α1 0.616 0.095 6.478 0.000 α2 -14.936 4.015 -3.720 0.001 α3 3.942 1.906 2.068 0.051 α4 0.454 0.109 4.164 0.000 R2 = 0.904 R2Ajust. = 0.887 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S    0RQHWDU\DQG)LVFDO%ORFN For simulation purposes, the interest rate follows a standard Taylor rule described in Equation 35, where γ1 is the weight on the persistence of the interest rate, γ2 is the weight on inflation and γ3 is the weight on the output gap. The variable LW(T is the long run equilibrium of the interest rate, and it was set to be around 6%. In the baseline scenario, the values were chosen in an ad-hoc manner and γ1 is 0.8, γ2 is 1.3 and γ3 is 0.8.   4 HW  (T .  LW = γ 1 ⋅ LW −1 + (1 − γ 1 )⋅ γ 2 ⋅ ∑ π W −L − π W7−arg L  + γ 3 ⋅ KW −1 + LW   L =1    ( ) (35) Although the traditional method of forecasting 6-month rates is by extracting information from the term structure, empirical results suggest that, due to the low liquidity in the market for futures contracts, yield curve information is not a good forecaster for future 6-month rates. Hence, we modeled the 6-month interest rate as a function of the contemporaneous Selic rate and contemporaneous and lagged risk premium values, as described in Equation 36. Outlier dummies were also used. The estimation outcome is shown in Table 17. Fiscal debt can be broken into three components: external fiscal debt, internal debt indexed to the change in exchange rate plus a risk premium, and internal debt denominated in the Selic rate. Thus, we modeled these fiscal debt components, subtracting the fiscal surplus, as in Equation 37. 6ZDS6 = α 0 + α 1 ⋅ 6ZDS6 −1 + α 2 ⋅ 6HOLF + α 3 ⋅ 6HOLF −1 + α 4 ⋅ ∆6&%RQG W W W 32 W W (36) ' ([W ' ,QW W W ( = ' −1 ⋅ 1 + L ([W W = ' −1 ,QW 1R W exchange rate variation W ' =' W W W W ( ,QW :LWK ([W )⋅ (1 + 5LVN ) ⋅ (1 + 6HOLF )+ ⋅ (1 + 5LVN )⋅ (1 + exchange rate variation W  + ' −1 I W +' ,QW W − )6 (  W ) W 7DEOH (TXDWLRQ 0HWKRG 2/6 6DPSOH 1988:01 to 2001:02 &RHIILFLHQW (VWLP9DOXH 6W'HYLDWLRQ W 39DOXH α0 0.029 0.008 3.599 0.001 α1 0.731 0.122 5.999 0.000 α2 0.416 0.151 2.764 0.008 α3 -0.293 0.078 -3.763 0.000 α4 2.054 0.487 4.215 0.000 D98:08 -0.038 0.019 -2.030 0.047 D99:01 0.043 0.013 3.230 0.002 D99:02 0.072 0.014 5.270 0.000 R2 = 0.955 R2Ajust. = 0.950 %UHXVFK*RGIUH\6HULDO&RUUHODWLRQ/07HVW ODJV )  S   -DUTXH%HUD1RUPDOLW\7HVW S   :KLWH+HWHURVNHGDVWLFLW\7HVW)  S    6LPXODWLRQV The model is simulated in a Matlab/Simulink environment until 2100:4, but we will only show the first 30 years of results for simplicity. Our closure rule is an ad-hoc end-point for the current account/GDP ratio, which brings us to a long-run equilibrium value for the real exchange rate. The current account surplus was set at 0% for the last period of the simulation. The primary fiscal surplus follows an exogenous vanishing path to the long run. We also assumed that world and domestic growth converge in the long run. In the first simulation, whose graphics are in the Appendix (see Simulation 1), we set different weights for the Taylor rule. The baseline simulation presents γ1, γ2 and γ3 as 0.85, 1.30 and 0.30, respectively. A more aggressive rule against inflation sets γ1, γ2 and γ3 equal to 0.85, 1.50 and 0.10, respectively, meaning more weight in the inflation gap from the target and less weight in the output gap. An opposite rule with higher weight on the output gap is γ1, γ2 and γ3 as 0.85, 1.10 and 0.50, respectively. The results show a good convergence of the model. Inflation goes toward the target, GDP grows close to the potential, and fiscal debt is decreasing in the medium run. The 33 (37) comparisons between the three Taylor rules show that the more aggressive monetary policy leads to lower GDP growth and a lower fiscal surplus. The second simulation (see Simulation 2) is presented in terms of impulse responses. Three types of impulse shocks are simulated: a temporary positive shock to the nominal Selic interest rate, a temporary positive shock to the C-Bond spread and a temporary positive shock to administered prices. An increase in the Selic interest rate has the greatest impact on inflation with a lag of 7 quarters. Risk premium shocks affect inflation through different channels. The first is the exchange rate channel, which causes an increase in inflation via the pass through channel. The second channel is the medium run interest rate; in this channel, an increase in the risk premium causes an increase in the medium term interest rate and a corresponding slight decrease in inflation (Swap06) via a decrease in the output gap and the GDP growth rate. But the average impact of an increase in the risk premium on inflation is positive until it vanishes in the long run. Administered price shocks cause an increase in inflation, as expected. Administered price shocks instantly decrease the real interest rate, increasing the GDP growth rate and inflation. But this is followed by an increase in the nominal interest rate, in order to bring inflation back to the target, which increases the real interest rate, decreasing the GDP growth rate. This oscillatory path of the GDP growth rate continues, depending on the weight of the output gap in the Taylor rule, but in a vanishing path. Those temporary shocks have temporary effects on the real exchange rate, but permanent effects on the nominal exchange rate. Positive risk premium and administered price shocks depreciate the nominal exchange rate while positive nominal interest rate shocks cause nominal appreciation. Positive nominal interest rate shocks increase the sovereign risk premium by worsening the public debt. Indeed, the effects of positive nominal interest rate shocks on public debt, although not permanent, take so long to vanish that they appear permanent. Positive administered price shocks decrease the public debt, as expected, via the inflationary tax effect. 34  &RQFOXVLRQDQG1H[W6WHSV The objective of this paper was to present the main features of the Keynesian macroeconomic model in development at the Central Bank of Brazil. As this paper is still a work in progress, we have many more steps to accomplish and close conclusions. The model with disaggregated demand and potential output with a production function demonstrates good convergence. We still can detect problems with the import and consumption equations. The simulations simultaneously brought about consistent paths for output, employment, inflation, the current account, the rate of investment and the fiscal balance. However the long-run equilibrium of some variables are dependent on the end-points for the interest rate and exchange rate. Another problem that we have with this kind of model is that it is not robust to the Lucas critique. Some of the parameters may vary through the sample period due to policy changes. Aware of this limitation we still consider Keynesian models useful tools for identifying the transmission mechanism of the monetary policy. The simulations have to be considered with caution especially for Brazilian economy, because there are many cases of structural breaks and policy swings. As future goals we can point out: • Consumption disaggregated in durable and non-durable goods; • A forward looking rational expectations term for inflation in the Phillips curve and for the exchange rate in the UIP equation; • More equations for the wage sector, using the Phillips curve that includes the unit labor cost; • A more structured fiscal block; • A production function with more than one kind of capital.    35 %LEOLRJUDSK\ Agenor, Pierre-Richard and Montiel Peter (1996) “Development Macroeconomics” Princeton University Press Alves, Sergio A. Lago (2001) “Evaluation of the Central Bank of Brazil Structural Model's Inflation Forecasts in an Inflation Targeting Framework” %DQFR&HQWUDOGR %UDVLO:RUNLQJ3DSHU6HULHV nº 16. Bansal, Ravi e Magnus Dahlquist (1999) “The Forward Premium Puzzle: Different Tales from Developed and Emerging Economies” &(35'LVFXVVLRQ3DSHU2169. Bogdanski, Joel, Tombini, Alexandre e Werlang Sergio (2000) “Implementing Inflation Targeting in Brazil” %DQFR&HQWUDOGR%UDVLO:RUNLQJ3DSHU6HULHV nº1. Boone, Laurence, Michel Juillard, Douglas Laxton and Papa N’Diaye (2002) “How Well Do Alternative Time-Varying Parameter Models Os The NAIRU Help Policymakers Forecasts Unemployment And Inflation In The OECD Countries?” ,0) :RUNLQJ 3DSHU, presented at the Eighth International Conference of The Society for Computational Economics, CEF2002 (Aix en Provence, France, June/2002). García, Carlos, Pablo García, Igal Magendzo e Jorge Restrepo (2002) “A Medium-Sized Macroeconometric Model of the Monetary Transmission Mechanism in Chile” &RQIHUHQFLD 0RGHORV 'H (TXLOLEULR *HQHUDO 3DUD /D (FRQRPtD &KLOHQD, organized by Central Bank of Chile (Santiago, Abril/2002) Cavalcanti, Marco A. F. H., Hamilton Kai and Leonardo Carvalho (2002) “Principais Características do Modelo Macroeconômico do IPEA” ,3($, seminary presented on June 26, 2002 Gonzaga Gustavo e Bevilacqua Afonso (1997) Relatório Consultoria da Banco Central do Brasil, mimeo Reis, Eustaquio, Cavalcanti Marco Antônio, Castro, Alexandre Rossi Jr. Jose Araújo Emerson e Hernandes Beatriz (1999) “Model for Projections and Simulations of the Brazilian Economy” ,3($7H[WRSDUD'LVFXVVmRQž McCallum, Ben. (1994) “ A Reconsideration of the Uncovered Interest Parity Relationship” -RXUQDORI0RQHWDU\(FRQRPLFV vol. 33 pp 105-132 36 Meredith, G. & Chinn, M. (1998): Long-Horizon Uncovered Interest Rate Parity, 1%(5:RUNLQJ3DSHU 6797 Min, Hong G. (1998). “Determinants of Emerging Markets Bond Spread: Do Economic Fundamentals Matter” World Bank mimeo. Muinhos, Marcelo & Alves, Sergio A. L. e Riella, Gil (2002) “Modelo Estrutural Com Setor Externo: Endogenização do Prêmio de Risco e do Câmbio” %DQFR&HQWUDOGR %UDVLO:RUNLQJ3DSHU6HULHV no 42. Muinhos, Marcelo & Freitas, Paulo e Araújo, Fabio (2001) “Uncovered Interest Parity with Fundamentals: A Brazilian Exchange Rate Forecast Model” %DQFR&HQWUDOGR %UDVLO:RUNLQJ3DSHU6HULHV nº19. Pastore Afonso e Pinotti Maria Cristina (1999) Boletim Periódico - ACC Pastore Consultoria Wadhwani, Sushil B. (1999) - &XUUHQF\3X]]OHV LSE Lecture on 16 September 1999 37 $SSHQGL[ 2EWDLQLQJD4XDUWHUO\9DOXHV)RU7KH3URGXFWLRQ)XQFWLRQ In order to obtain quarterly values for α, three alternatives were available. The first is to maintain the annual values in each quarter. However, as the resulting quarterly series present a step shaped pattern, with abrupt level changes on the first quarter of every year, this alternative was discarded because we expect a smoother behavior. A natural choice, as a second alternative, is to consider a filtered series, obtained by a HP filter, for instance, instead of the original one. Again, however, this resulted in a undesired behavior: although the average quarterly values of each year should be equal to the original annual values, this was not the case when using the regular filtering process. Hence, we considered a third alternative that assured the following two features: the smoothness and the restriction on the average of the annual quarterly values. This alternative was based on the quarterly data generating process, based on an annual frequency data, presented in Alves (2001) and is described in System 38.    $ ≡ Annual capital share yield series, with n observations $ W ≡ Particular value for α $ in year t : t ∈ [1, n ] One wishes to estimate the quarterly capital share yield series α 4 such as:    4 4 W4 4 , W 4 ≡ Quarterly capital share yield series, with 4n observations ≡ Particular value for 4 in quarter Q of year t : t ∈ [1, n ], Q ∈ [1, 4] series should ensure that:   Minimize   Subject to  L = ∑∑ (∆ 2 Q W =1 4 ∑ Q =1 4 W4 4 4 4 W4 =1 = 4⋅  38 4 W , ) 2 ∀ t ∈ [1, Q ] (38) $SSHQGL[ 6LPXODWLRQ*UDSKLFV 6LPXODWLRQ  ,QIODWLRQ                          WD \ORU                           WD \ORU            WD \ORU     *'3      WD\ORU  WD\ORU                                               WD\ORU   5HDO,QWHUHVW5DWH                          WD \ORU                      WD\ORU  39                     WD \ORU   5HDO([F5DWH                                WD\ORU                          WD\ORU                    1RPLQDO([F5DWH WD\ORU                          WD \ORU                          WD\ORU                    WD \ORU   3XEOLF'HEW                     WD\ORU                      WD\ORU   40                     WD\ORU  6LPXODWLRQ (Quarters in horizontal axis)  ,QIODWLRQ                      6K6HOLF 6K5LVN 6K$GP  *'3                6K6HOLF 6K5LVN 6K$GP  1RPLQDO,QWHUHVW5DWH                    6K6HOLF 6K5LVN 41 6K$GP    5,6. EE                6K6HOLF 6K5LVN 6K$GP  5HDO([F5DWH               6K6HOLF 6K5LVN 6K$GP  1RPLQDO([F5DWH               6K6HOLF 6K5LVN 42 6K$GP    3XEOLF'HEW                     6K6HOLF 6K5LVN 6K$GP  5HDO,QWHUHVW5DWH                     6K6HOLF 6K5LVN 43 6K$GP   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 e Sérgio Ribeiro da Costa Werlang Jul/2000 2 Política Monetária e Supervisão do Sistema Financeiro Nacional no Banco Central do Brasil Eduardo Lundberg Jul/2000 Monetary Policy and Banking Supervision Functions on the Central Bank Eduardo Lundberg 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 e Sérgio Ribeiro da Costa Werlang Jul/2000 6 Optimal Interest Rate Rules in Inflation Targeting Frameworks José Alvaro Rodrigues Neto, Fabio Araújo e Marta Baltar J. Moreira Jul/2000 7 Leading Indicators of Inflation for Brazil Marcelle Chauvet Set/2000 8 The Correlation Matrix of the Brazilian Central Bank’s Standard Model for Interest Rate Market Risk José Alvaro Rodrigues Neto Set/2000 9 Estimating Exchange Market Pressure and Intervention Activity Emanuel-Werner Kohlscheen Nov/2000 10 Análise do Financiamento Externo a Uma Pequena Economia 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 e Stephen G. Cecchetti Mar/2001 12 A Test of Competition in Brazilian Banking Márcio I. Nakane Mar/2001 44 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 e 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 Mar/2001 Evaluation of the Central Bank of Brazil Structural Model’s Inflation Forecasts in an Inflation Targeting Framework Sergio Afonso Lago Alves Jul/2001 Estimando o Produto Potencial Brasileiro: Uma Abordagem de Função de Produção Tito Nícias Teixeira da Silva Filho Abr/2001 Estimating Brazilian Potential Output: A Production Function Approach Tito Nícias Teixeira da Silva Filho Ago/2002 18 A Simple Model for Inflation Targeting in Brazil Paulo Springer de Freitas e Marcelo Kfoury Muinhos Abr/2001 19 Uncovered Interest Parity with Fundamentals: A Brazilian Exchange Rate Forecast Model Marcelo Kfoury Muinhos, Paulo Springer de Freitas e Fabio Araújo Maio/2001 20 Credit Channel without the LM Curve Victorio Y. T. Chu e Márcio I. Nakane Maio/2001 21 Os Impactos Econômicos da CPMF: Teoria e Evidência Pedro H. Albuquerque Jun/2001 22 Decentralized Portfolio Management Paulo Coutinho e 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 e Alexandre Antonio Tombini Ago/2001 25 Inflation Targeting in Brazil: Reviewing Two Years of Monetary Policy 1999/00 Pedro Fachada Ago/2001 26 Inflation Targeting in an Open Financially Integrated Emerging Economy: the case of Brazil Marcelo Kfoury Muinhos Ago/2001 17 45 27 Complementaridade e Fungibilidade dos Fluxos de Capitais Internacionais Carlos Hamilton Vasconcelos Araújo e Renato Galvão Flôres Júnior Set/2001 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 e Solange Gouvêa Nov/2001 30 Testing the Expectations Hypothesis in the Brazilian Term Structure of Interest Rates Benjamin Miranda Tabak e 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 e 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 Fev/2002 37 Monetary Policy in Brazil: Remarks on the Inflation Targeting Regime, Public Debt Management and Open Market Operations Luiz Fernando Figueiredo, Pedro Fachada e 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 e Márcia Leon Abr/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 46 43 The Effects of the Brazilian ADRs Program on Domestic Market Efficiency Benjamin Miranda Tabak e Eduardo José Araújo Lima Jun/2002 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 Ago/2002 46 The Determinants of Bank Interest Spread in Brazil Tarsila Segalla Afanasieff, Priscilla Maria Villa Lhacer e Márcio I. Nakane Ago/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 e Marcos Antonio Silveira Set/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 TwoCountry Model Eui Jung Chang, Marcelo Kfoury Muinhos e Joanílio Rodolpho Teixeira Set/2002 51 Credit Channel with Sovereign Credit Risk: an Empirical Test Victorio Yi Tson Chu Set/2002 52 Generalized Hyperbolic Distributions and Brazilian Data José Fajardo e Aquiles Farias Set/2002 53 Inflation Targeting in Brazil: Lessons and Challenges André Minella, Paulo Springer de Freitas, Ilan Goldfajn e Marcelo Kfoury Muinhos Nov/2002 54 Stock Returns and Volatility Benjamin Miranda Tabak e 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 e Eduardo José Araújo Lima Dez/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 Dez/2002 59 Os Preços Administrados e a Inflação no Brasil Francisco Marcos R. Figueiredo e Thaís Porto Ferreira Dez/2002 47 60 Delegated Portfolio Management Paulo Coutinho e Benjamin Miranda Tabak Dez/2002 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 Jan/2003 63 Optimal Monetary Rules: The Case of Brazil Charles Lima de Almeida, Marco Aurélio Peres, Geraldo da Silva e Souza e Benjamin Miranda Tabak Jan/2003 48