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Volume 17, Issue 2


Do Latin American Central Bankers Behave Non-Linearly? The Experiences of Brazil, Chile, Colombia and Mexico

Luiz de Mello / Diego Moccero / Matteo Mogliani
  • Banque de France, 46-1383 DGEI-DCPM-DIACONJ, 31 Rue Croix des Petits Champs, 75049 Paris Cedex 01, France
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Published Online: 2013-04-11 | DOI: https://doi.org/10.1515/snde-2012-0063


This paper contributes to the empirical literature on inflation zone targeting by estimating monetary reaction functions in a non-linear cointegration framework for Brazil, Chile, Colombia and Mexico. Evidence shows that central banks respond linearly to deviations of expected inflation from the target (the inflation gap) in Brazil and Chile. As the inflation gap widens, policy responses become weaker in Colombia and Mexico, a finding that most probably reflects a history of adverse supply shocks rather than a lack of resolve from the monetary authorities. Non-linearity is also found in the central bank’s response to fluctuations in the exchange rate in Brazil and Colombia.

Keywords: inflation zone targeting; non-linear cointegration; reaction function; smooth transition models; JEL-Codes: C22; E52; O54


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About the article

Corresponding author: Diego Moccero, European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany

Published Online: 2013-04-11

For example, Erceg (2002) shows that the optimal width of an inflation band in an open economy increases with the strength of terms of trade shocks. Similarly, Mishkin and Westelius (2008) find that more uncertain inflation leads to wider target ranges. See Castelnuovo, Nicoletti-Altimari, and Rodriguez-Palenzuela (2003) for a discussion of the pros and cons of ranges versus point inflation targets and for a review of operational practices for inflation targeting in developed countries.

Evidence seems to support this hypothesis for the United States. Barnes and Olivei (2003) find that inflation does not react to the unemployment gap over a range of values, but a significant trade-off emerges outside this range.

This is because, under uncertainty, there is always a probability that a shock will drive inflation outside the target zone, prompting an immediate policy reaction.

Tachibana (2006, 2008) notes that both the United States and Japan have implemented implicit inflation zone targeting since neither the US Fed nor the Bank of Japan has adopted explicit inflation targeting regimes.

Monetary policy reaction functions that include the exchange rate have been estimated by Mishkin and Savastano (2001) and Mohanty and Klau (2005), among others. The monetary authorities are hypothesized to care about the exchange rate and its variability because of their impact on inflation (via relative prices and expectations, for instance); on the performance of the external sector, investment and growth (via trade competitiveness); on financial and public debt sustainability (via balance-sheet effects) and on the development of foreign-exchange and capital markets. See Ho and McCauley (2003) for a comprehensive study including both developed and developing country inflation targeters.

For a detailed description of monetary-policy instruments in these countries, see Figueiredo, Fachada, and Goldenstein (2002) for Brazil; Cifuentes and Desormeaux (2005) and Loayza and Schmidt-Hebbel (2002) for Chile; Uribe (1999), Vargas (2005), Melo and Riascos (2004) and Clavijo (2004) for Colombia; and Ramos-Francia and Torres (2005) and Central Bank of Mexico (2007) for Mexico.

While the target horizon of the monetary authorities in Chile and Colombia is about two years, there is no explicit reference to a specific target horizon in the case of Brazil and Mexico. However, these central banks have tended to highlight in their communication with the public the behavior of 12-month ahead, survey-based measures of inflation expectations (see, for example, Central Bank of Mexico 2003).

It is important to note that central banks might not react only to market expectations, but also to their own inflation projections. Indeed, forecasts of consumer inflation rates are published by central banks in their Inflation Reports in the four countries under consideration. However, two features make these forecasts unsuitable for use in econometric analysis: i) they are only available to the public on a quarterly basis, while the monetary authorities meet eight times per year in Brazil and Mexico, and every month in Chile and Colombia. This mismatch in the data frequency may result in poor estimates of the policy reaction functions; and ii) inflation forecasts are reported for a fixed target date horizon only (end-year inflation rates for the next two years). This implies that the length of the forecast window becomes shorter within a cycle of forecasts and then reverts back to the initial length to begin another forecast cycle. This feature reduces the comparability of adjacent surveys.

There is some debate about whether or not inflation (and inflation expectations) can be integrated of order one. Some interpret the unit root finding as central bank failure to anchor inflation (expectations) around point inflation targets, even in the long run. In our view, the unit root finding owes much to the high share of food and energy in the consumption basket of developing countries, and substantial supply-side shocks which are characteristic of small open economies. Moreover, monetary authorities in these countries have been highly successful in keeping inflation rates within the inflation bands, over most of the inflation targeting period (see de Mello and Moccero 2009).

This is a main difference with respect to monetary reaction functions estimated for developed economies, where both the policy interest rate and the output gap are assumed to be stationary.

The main advantages of these error-correction-based methodologies are twofold (Ericsson and MacKinnon 2002). First, the long-run coefficients (on which the hypothesis of cointegration is tested) are not biased, due to the inclusion of the short-run dynamics of the model into the test equation. Second, no restrictions are imposed on the long- and the short-run coefficients, given that the equilibrium and the dynamic relationships described by the model are estimated simultaneously. In addition, a desirable feature of PSS bounds testing approach is that the existence of long-run relationships among a set of covariates can be tested while being agnostic about the order of integration of the relevant variables. The test procedure is then applicable whenever the regressors are I(1), I(0) or mutually cointegrated.

The restriction over the deterministic trends is necessary in our testing strategy. Indeed, the PSS statistic we use for testing the presence of a long-run relationship sets the trend coefficient to zero under the null hypothesis. If the trend coefficient δ was not subject to this restriction, Equation (3) would imply a quadratic trend in the level of policy interest rates under the null hypothesis of λ=0 and β=0, which is empirically implausible.

The appreciation of the exchange rate during the period under analysis is related to an improvement in terms-of-trade, an increase in net factor income from abroad and a rise in direct foreign investments (in oil extraction-related activities and the privatization of several state-owned companies). See Central Bank of Colombia (2007, 2008), for an analysis of recent exchange rate dynamics in Colombia.

When γ→+∞, the reaction function becomes

, if
, if

Assumption b) is criticized by Saikkonen and Choi (2004) and Choi and Saikkonen (2010), who develop a NLLS asymptotic theory based on the triangular array asymptotics. Such asymptotic theory exhibits suitable limiting properties for the case of smooth transition parameters, and seems to overperform the limiting theory exposed in Chang and Park (2003). Moreover, simulation results in Saikkonen and Choi (2004) suggest that a Gauss-Newton estimator performs better than a simple NLLS estimator, mainly in an efficient lead-and-lags regression problem. However, for reasons discussed in footnote (18), we do not implement such estimator.

As mentioned before, while γ is a free parameter, restricted to be greater than zero, c must lie between the minimum and the maximum values of the transition variable to be economically interpretable. We therefore fix γ equal to 1 and c equal to 0, which lies between the maximum and the minimum values of the inflation gap for Brazil and is very close to the minimum value for Colombia and Mexico, as initial values for the NLLS estimations.

Park and Phillips (2001) show that least-square regressions are consistent even when the model is non-linear, but the rates of convergence can differ from the case of regressions with stationary data. Also, in a multivariate setting the asymptotic distribution of the NLLS estimator is in general non-Gaussian, which implies that standard hypothesis testing is invalid. Only in the special case where the integrated regressors are strictly exogenous, the asymptotic distribution of the NLLS estimator is mixed-normal.

Another theoretically efficient estimator consists of including leads and lags of the first-differenced regressors, as suggested by Saikkonen and Choi (2004) and Choi and Saikkonen (2010). We experimented with the leads-and-lags estimator, using one lead and lag for each non-stationary regressor, and the results (not reported) are consistent with those obtained on the basis of the EN-NLLS estimator. However, it was difficult to estimate the regressions with more than one lead and lag because of the fall in the degrees of freedom resulting from the inclusion of additional parameters.

The procedure is akin to the Shin (1994) test for the null of cointegration, following the tradition of the Kwiatkowski etal. (1992) univariate test for the null of stationarity.

The cumulative distribution function of

takes the following form:
is the error function of a Gaussian distribution and the series is truncated at small n (we follow Choi and Saikkonen, 2010 and set n=10).

The significance of this parameter, although reported in Table 4, is hardly interpretable, because we cannot use conventional hypothesis testing for the parameters inducing non-linearity due to identification issues (Saikkonen and Choi 2004).

It follows from Theorems 4.1 and 5.1 in Park and Phillips (2001) and from Chang, Park, and Phillips (2001) that standard hypothesis testing, such as Wald tests, is valid for parameters in both linear and non-linear part of the model.

Fraga, Goldfajn, and Minella (2003) present evidence suggesting that inflation targeting emerging-market economies perform less well than developed economies because inflation targeting is more challenging in the former than in the latter, rather than because of lack of commitment.

Although the magnitude of the smoothness parameter is similar in both countries, the transition functions for Colombia and Brazil are different because the scale factor (

) is larger for Brazil.

The monetary policy response coefficients to the inflation gap may look high in the cases of Colombia and Mexico. However, it should be reminded that coefficients depend on the scale of the dependent and explanatory variables. In Colombia, the average policy interest rate over the estimation period amounts to close to 7%, while the average of the expected inflation gap is low, at close to 0.45%. Hence, the difference in scale between the two variables results in a high response coefficient in the monetary policy reaction function. A similar reasoning can be applied to the case of Mexico.

Since the objective function is continuous on Θ and the parameter space is compact and convex, the NLLS estimator of parameters exists and is Borel measurable (Pötscher and Prucha 1997).

Citation Information: Studies in Nonlinear Dynamics and Econometrics, Volume 17, Issue 2, Pages 141–165, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2012-0063.

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