Abstract
We investigate the existence of an asymmetry in the exchange rate pass-through to the Brazilian consumer price index (CPI). Using a decomposition of the exchange rate series, into appreciations and depreciations of the Brazilian currency during the 1999–2016 period, we estimate Structural Vector Auto-regression (SVAR) models with different identifying restrictions. The results are robust and indicate a relevant asymmetric behavior of the exchange rate pass-through. Estimates indicate a pass-through of 16% in case of depreciation and of 5.8% in case of appreciation of Brazilian Real (BRL) against the US Dollar. Accordingly, the inflationary effect resulted from a (systematic) depreciation is only partially compensated by a deflationary effect of an (systematic) appreciation of the same magnitude, generating an inflationary bias that may cast doubts on inflation control strategies based solely on inflation targeting. Results provide a case against excess exchange volatility and capital mobility. A stable exchange rate favors price stability.
Keywords
- Exchange Rate Pass-through
- Inflation Dynamics
- Exchange Rate Series (ER)
- Brazilian Currency
- Institute For Applied Economic Research (IPEA)
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- 1.
In Portuguese, Banco Central do Brasil.
- 2.
Calculated by the Brazilian Institute of Geography and Statistics (IBGE) and considered the official inflation index of the country.
- 3.
In Brazil, the basic interest rate goes by the acronym (Selic) for Sistema Especial de Liquidação e de Custódia (Special System for Settlement and Custody ), which is the settlement system for most domestic securities of the Brazilian government.
- 4.
The New Consensus on Macroeconomics (Blinder 1981, 1998; Taylor 1993, 2000; Allsopp e Vines 2000; Romer 2000) is associated with the growing popularity of inflation targeting and the resulting acceptance that, even where the regime is not adopted, the main instrument of monetary policy is the (basic) interest rate, and no longer the monetary aggregates of some decades ago, influenced by monetarism. The new consensus theoretical core is given by the confluence of monetarism, new classical, and real business cycle theories. The natural rate of unemployment (Friedman 1968) and rational expectations hypothesis are among the two most relevant assumptions shared by this large group of economists. Another fundamental part is the Taylor rule —which holds that the central banks should determine its interest rate aiming at an explicit or implicit inflation target, and at keeping GDP growth near to its potential. We agree with Lavoie that “the only truly new element in the new consensus […] is the rejection of the exogenous supply of money, and the replacement of money growth rule for a real interest rate targeting rule […]” (Lavoie 2004, p. 23).
- 5.
For details on the role of foreign exchange derivative market in Brazil, see Chap. “Foreign Exchange Derivatives and Financial Fragility in Brazil” of this book by Maryse Farhi.
- 6.
According to existing literature (Modenesi and Modenesi 2012): among the main empirical-institutional features of Brazilian economy that compromises the monetary policy transmission, these are noteworthy: (i) nonexistence of a yield curve for sufficiently long maturity periods; (ii) the high share of administered prices in the IPCA; (iii) existence of a perverse cost channel; and (iv) the so-called LFT problem (Modenesi and Modenesi 2012). LFT (Letras Financeiras do Tesouro, in Portuguese) is a special kind of government bonds that are indexed to Selic.
- 7.
Even recognizing that Brazil’s rates of growth in the 1980s were low, one cannot deny that monetary policy has, at least, constituted a relevant hindrance to the reversal of this situation.
- 8.
Administered prices represent around 30% of CPI in Brazil. Many of them are (directly or indirectly) indexed to exchange rate. One should note that not all administrated prices are indexed to past inflation.
- 9.
In the McCarthy (2007) model, inflation is determined by “supply” shocks, “demand” shocks, and the exchange rate.
- 10.
One should conclude, that in both studies, the results showed that exchange rate pass-through was higher during periods of depreciation of the local currency than in periods of appreciation.
- 11.
Under the so-called normal regime, the pass-through to consumer prices was not statistically significant. Comparatively, the expected pass-through under a “crisis” regime is of 10%. “Crisis” periods occurred from 2000 to 2003 and in 2015, years in which the BRL depreciated. The “normal” cycle extends from 2003 to 2014, years of continuous appreciation of the local currency (except for July to November 2008).
- 12.
For instance, Brun-Aguerre et al. (2017), Pollard and Coughlin (2003), Herzberg et al. (2003), Bussiere (2013), Webber (1999), Wickremasinghe and Silvapulle (2004), Campa et al. (2008), Alvarez et al. (2008), Gil-Pareja (2000) and Karoro et al. (2009), estimate asymmetric exchange rate pass-through to import prices. Khundrakpam (2007) employ producer prices. Mihaljek and Klau (2008), Przystupa and Wróbel (2011) and Delatte and Villavicencio (2012) utilize asymmetric exchange rate pass-through to consumer prices. All these papers decompose the exchange rate in appreciations and depreciations.
- 13.
Sometimes it also refers to the speed that exchange rate fluctuations affect prices.
- 14.
According to Goldfajn and Werlang (2000) and Calvo and Reinhart (2000) ERTP is higher for the emerging countries than for developed countries. Additionally, in emerging countries, with currencies placed at the lower end of the currency hierarchy, exchange rate is prone to be more volatile (Paula et al. 2017).
- 15.
“Most recent empirical studies of monetary policy and real economic activity have adopted a vector autoregression (VAR)” (Walsh 2003, 24).
- 16.
For details on the SVAR models used, and the decomposition of the exchange rate series (ER) into ER+ and ER− see appendix.
- 17.
Residuals that are not autocorrelated, nor heteroscedastic, and are normally distributed. For residual autocorrelation Portmanteau and Lagrange Multiplier tests were performed. For residual normality, the multivariate Jarque-Bera and White’s test for heteroscedasticity of residuals.
- 18.
The same structural factorization used to calculate impulse response functions was used in variance decomposition.
- 19.
The simulated indexes are a partial analysis that only considers the impact of exchange rate variations on the IPCA for comparative purposes, not considering other factors also important for the dynamics of the Brazilian inflation rate. The upward trend shown by the simulated asymmetric index resembles much more the observed trajectory of actual IPCA.
- 20.
It is necessary to impose \({{K\left( {K + 1} \right)} \mathord{\left/ {\vphantom {{K\left( {K + 1} \right)} 2}} \right. \kern-0pt} 2}\) restrictions on both matrices A and B to satisfy order condition. The order condition is necessary for identification but may not suffice if rank condition fail. Rubio-Ramirez et al. (2010) discuss rank conditions for identification in SVAR models.
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Appendix
Appendix
1.1 SVAR Model
Consider a K-dimensional time series \(Y_{t} = \left( {y_{1} ,y_{2} , y_{3} ,y_{4} } \right)^{'}\) where Y t is a SVAR of finite order p of the structural form
where A is a K × K matrix that defines the causal interrelationships among the contemporaneous variables, and u t denotes a mean zero uncorrelated error term (also referred to as structural innovation or structural shock) with a variance-covariance matrix \(E\left( {u_{t} ,u_{t}^{\prime } } \right) =\Sigma _{u}\). Because structural shocks are by definition uncorrelated, \(\Sigma _{u}\) is a diagonal matrix (Kilian 2011).
Equation (1) cannot be estimated by ordinary least squares (OLS) since the variables have contemporaneous effects on each other. OLS estimates would suffer from simultaneous equation bias since the regressors and error terms would be correlated (Enders 2014).
In order to allow estimation, it is necessary to derive its reduced form representation. Premultiplication on both sides of Eq. (1) by A −1 allows the reduced form (2) to be obtained.
Where \(c_{0} = A^{ - 1} v_{0} ;\quad\Phi _{i} = A^{ - 1} B_{i} ;\quad Ae_{t} = Bu_{t}\).
Standard OLS method obtains consistent estimates of the reduced form (2) parameters \(\Phi _{i}\), the reduced form errors e t and their covariance matrix \(E\left( {e_{t} e_{t}^{\prime } } \right) =\Sigma _{e}\) (Lütkepohl 2005).
However, the reduced form errors are correlated. Only in the special case where there are no contemporaneous effects among variables (i.e., matrix A elements, \(a_{ij} (i \ne j)\), equals zero) the shocks will be uncorrelated.
It is possible, however, to recover the structural VAR coefficients and analyze how Y t respond to structural shocks in u t , from the estimates of the model in reduced form since, by construction, \(Ae_{t} = Bu_{t}\). Hence, the variance of e t is
\(\Sigma _{e}\) can be consistently estimated from the reduced form by OLS, and the system can be solved for the unknown parameters provided that the number of unknown parameters do not exceed the number of equations. This involves imposing restrictions on matrix A. Usually, the most common approach is to impose a ij = 0 restrictions (Kilian 2011).Footnote 20
The assumption a ij = 0 means that yj does not have a contemporaneous effect on yi. The imposition of different restrictions will result in different impulse response functions depending on the correlation between errors in the reduced form. Only if all reduced form errors are uncorrelated impulse response functions will be the same regardless of the restrictions imposed.
1.1.1 Asymmetry
One possible approach to investigate the existence of asymmetric effects of x t on y t is to decompose the variable x t into two new series: \(x_{t}^{ + }\) of its positive variations and \(x_{t}^{ - }\) of the negative variations.
Based on Schorderet (2004) and Granger and Yoon (2002) method, a time series can be decomposed as follows:
Where
Such as that, x t value, for all t, is equal to its initial value (x 0) plus the sum of all its positive and negative variations up to t.
In this way, we have first difference of \(x_{t}^{ + }\) and \(x_{t}^{ - }\) series:
The decomposition in form (5) and (6) is known in literature as decomposition by cumulative variations whereas the form in (7) and (8) is known as period-to-period variations.
Series decomposed by cumulative variations have unit root and cointegrate and are used in the estimation of error correction models (ECM) and its multivariate form vector error correction (VEC).
For purpose of this chapter, that estimates a model with the stationary variables in first difference, the most adequate decomposition, that was used, is the period-to-period decomposition.
1.1.2 Exchange Rate Pass-Through
The exchange rate pass-through can be calculated from impulse response functions estimated by the SVAR model. This method was used by McCarthy (2007) to calculate the exchange rate pass-through for several industrialized countries and by Belaisch (2003) and Araújo and Modenesi (2010) for Brazil.
Where ΔCPI is consumer price index variations and ΔER exchange rate variations.
1.1.3 Wald Coefficient Restriction Test
Wald coefficient restriction tests were performed in asymmetric models to test the hypothesis that the coefficients relative to exchange rate positive variations are statistically different from the negative variations.
The test was performed under two different null hypothesis specifications:
- H 0 (A):
-
Null hypothesis that the sum of the coefficients of \(x^{ + }\) lags is equal to the sum of the coefficients of \(x^{ - }\) lags.
- H 0 (B):
-
Null hypothesis that the lag coefficient i of y + is equal to the lag coefficient i of \(y^{ - }\) for all lags.
To illustrate, generically, a two lags model, SVAR (2), and three variables, \(Y_{t} = \left( {y_{1}^{ + } ,y_{1}^{ - } ,y_{2} } \right)^{'}\), where \(y_{1}^{ + }\) and \(y_{1}^{ - }\) are period-to-period decompositions of \(y_{1}\)
In reduced form:
Can be written in the form
The Wald test was then calculated under H 0 with two different specifications
H 0 (A):
H 0 (B):
Under H 0, the Wald statistic is asymptotically distributed as a χ 2(q), where q is the number of linear restrictions.
Wald test statistics reject the null hypothesis that coefficients are equal at conventional significance levels. Under the null hypothesis A, the test statistic was 8.38 (0.08 p-value). Under the null hypothesis B, test statistic was 16.57 (0.03 p-value). Therefore, results indicate the existence of asymmetry, that is, that exchange rate devaluations have different effects on inflation than exchange rate appreciations.
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de Melo Modenesi, A., Luporini, V., Pimentel, D. (2017). Asymmetric Exchange Rate Pass-Through: Evidence, Inflation Dynamics and Policy Implications for Brazil (1999–2016). In: Arestis, P., Troncoso Baltar, C., Prates, D. (eds) The Brazilian Economy since the Great Financial Crisis of 2007/2008. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-64885-9_4
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