Inflation Targeting in Latin America: Post-Crisis Changes (Part 1)

Inflation Targeting in Latin America: Did Anything Change After the Crisis? Abstract After Chile, Brazil and Mexico’s adoption of Inflation Targeting (IT), inflation declined and monetary policy became a powerful countercyclical tool. The 2008 crisis tested this ability and, in its aftermath, a debate emerged over whether policy makers were undermining the regime. This paper explores whether monetary policy changed after the crisis and if it is a result from changes in the economic environment or in policy makers’ preferences. We first look at the gains that followed the adoption of IT and the behavior of key variables after the 2008 global financial crisis. A critical finding is that in two of the three countries the “neutral” real interest rate has fallen sharply. We first conclude that there have been changes in the monetary policy of these countries. Then, we estimate a structural VAR to analyze the dynamics of our focus variable, the policy rate, in response to shocks in key driving forces. Our tests find significant changes in the variance of output and inflation shocks after September 2008. We also analyze the Impulse Response Functions for interest rates in response to different shocks. In Mexico, we find policy rates became more responsive to output than to inflation. In Brazil, we find little evidence of changes in the responsiveness of monetary policy to output or inflation shocks. Chile’s central bank seems somewhat quicker to respond to inflationary shocks. Keywords: Inflation Targeting, Monetary Policy, Reaction Function, Financial Crisis 2012     Table of Contents   1 Introduction 2 2 Literature Review 5 2.1 Policy Reaction Functions 5 2.2 Monetary Policy under Inflation Targeting 7 3 Modeling a Reaction Function 10 3.1 A Very Basic Model 10 3.2 Data and Methods of Measurement 13 3.2.1 Data 13 3.2.2 Potential Problems with Non-Stationarity 14 3.2.3 Time-varying neutral real interest rates 16 4 Results 21 4.1 Estimations for Full-Sample 21 4.2 Policy Rules and the Financial Crisis 23 4.3 Stability 24 5 A More Structural Approach 27 5.1 SVAR Specification 28 5.2 Results 29 5.2.1 Change in Residuals 29 5.3.1 Dynamic Response to Shocks 32 6 Conclusions 36 Appendix 39 References 47             2     1 Introduction During the 80s and early 90s, Latin American economies averaged the highest inflation rates in the world accompanied with overall high macroeconomic volatility. The policies in place undermined monetary credibility, lacked transparency and were characterized by high fiscal spending. The “Lost Decade,” as is popularly known in the region, is remembered by a crumbling debt crisis and many frequent maxi-devaluations. However, in a relatively brief period of time, that picture changed significantly as the region set forth on a new monetary and fiscal direction with price stability in mind. By 2005 most countries were exhibiting low to moderate inflation rates while maintaining high growth and, above all, gaining the ability to use counter-cyclical monetary policies. Among those that faired best in the region were the few that adopted an Inflation Targeting (IT) regime following the emerging popularity in advanced economies. In fact, Schmidt-Hebbel and Werner (2002) attribute much of the success in price stabilization to the gain in credibility brought about by the commitment to IT. Neumann and von Hagen (2002) add that although both ITers and non-ITers improved over time, on average, ITers reduced inflation by more and converged to similar levels. The evidence on IT’s success has, however, been widely contested. Examining Latin America, McDermott and McMenamin (2008) suggest that there is no robust statistically significant difference in the benefits of IT and non-IT regimes when considering the fortuitous international inflationary environment of the past decade, commonly known as the “Great Moderation.” (See Cecchetti and Ehrmann (2002) and Broto (2008)). Moreover, Ball and Sheridan (2003) have claimed that Neumann and von Hagen’s argument about the merits of inflation targeting is best explained by a case of   3     regression to the mean, where countries with unusually high and unstable inflation tend to see these problems diminish, regardless of their regime. The skepticism notwithstanding, during a speech in 2003, Bernanke acknowledged the widespread appeal of this new regime and concluded that its success is best described by its increasing adoption and implementation: “Central banks that have switched to inflation targeting have generally been pleased with the results they have obtained. The strongest evidence on that score is that, thus far at least, none of the several dozen adopters of inflation targeting has abandoned the approach.” However, with the late financial crisis the era of the Great Moderation came to an end, putting Bernanke’s claim to a test. Was the IT framework resilient to a crisis that caused a significant increase in volatility of real and financial variables or did central banks step back? This paper intends to evaluate if there has been a meaningful change in the implementation of monetary policy brought about by the recent events and external shocks for three IT countries in Latin America - Brazil, Chile and Mexico. Furthermore, we evaluate whether these changes (or lack thereof) reflect a natural adaptation of policy rules to align with the recommendations that would emanate from first principles, or alternatively, whether they reflect changes in the preferences of policymakers. Our research tests the stability of the policy reaction function in the period that follows the September 2008 financial crisis. To do so, we formulate Taylor-like reaction functions and test the stability and direction of the observed changes. We then take the empirical reaction function approach one step further and estimate structural vector autoregressions, attempting to identify the sources and nature of the changes observed.   4     We find that inflation targeting in the region has indeed evolved. All countries have over time changed the way they conduct their policies. Chile and Brazil, currently target expected inflation while Mexico appears to remain more focused on actual inflation. More importantly, we find that Chile responds with less of a lag to shocks, a finding that when tested in greater detail, seems consistent with an optimal adaptation to uncertainty about inflation. We also find some evidence of changes in the way Brazil conducts its IT regime, responding more slowly to changes in expected inflation, but eventually with greater movements in policy rates. However, the evidence points to Brazil having had a much more meaningful change in the way IT was implemented after its home-grown fiscal/debt crisis of 2002-03. In Mexico, we find some mild evidence of a shift towards prioritizing somewhat more output movements over inflation. The remainder of the paper is as follows. Section 2 outlines the main literature on IT and policy rules. Section 3 develops a reduced-form model to estimate a policy rule and describes the data. A key contribution of our methodology is to allow for timevarying neutral interest rates. In section 4 we provide the empirical estimates and tests for structural breaks in the model. Section 5 follows by estimating a structural vector autoregressive specification. Section 6 concludes. 2 Literature Review 2.1 Policy Reaction Functions Monetary policy appraisal has grown dramatically since the emergence of the rational expectations hypothesis. Among the many innovations, macroeconomists placed greater emphasis on intertemporal minimization of loss functions that result in optimal reaction   5     functions. In a pioneering (empirical) description of the Fed’s reaction function, Taylor (1993) designed a simple, consistent policy rule that expressed the central bank’s instrument – in this case the federal funds rate – as a function of inflation deviations from the implicit target, output gap and a constant neutral real interest rate. Much of the empirical research that followed Taylor’s contribution focused on estimating the parameters of different central banks and testing the consistency of monetary policy responses. Among the many works, Clarida, Gali and Gertler (1999) develop a more comprehensive Taylor-type rule from first principles of a neo-Keynesian macroeconomic framework to evaluate Fed responses before and after the Volcker Era (see Judd and Rudebusch (1998), Woglom (2003) for more central bank reaction function estimations). Moreover, further research by Levin, Wieland and Williams (1999) has determined that these reaction functions are quite robust when it comes to evaluating optimal performance in a wide range of policy preferences. However, reaction functions have met their fair share of opposition. In an extensive paper focusing on the issues surrounding Taylor rules, Svensson (2003) argues that commitment to these rules are neither practical nor realistic, and therefore, should not be used to model central banking behavior. Furthermore, he suggests that the interpretation of these rules are limited by the Lucas Critique since standing by themselves they are only reduced-form models of endogenous variables. Indeed, Svensson’s critiques are well grounded and should not be taken lightly; however, in this paper we limit the interpretations we make from the reaction function in its reduced-form and complement our analysis through the use of a structural model.   6     2.2 Policy under Inflation Targeting Much of the discussion on Taylor-type rules has centered on the emergence of IT as a new monetary policy regime with the sole objective of maintaining price stability. In light of this discussion, Mishkin and Savastano (2001) define an IT regime as encompassing five main elements: The central bank must (i) publicly announce a medium-term numerical target for inflation; (ii) commit itself to pursue price stability as the primary goal; (iii) formulate an information-inclusive strategy in which many variables are used for deciding the setting of policy instruments; (iv) increase transparency of the monetary policy strategy through communication with the markets; and (v) increase accountability for attaining its inflation objectives. Furthermore, Svensson (1996) aligns IT with rational-expectations by referring to it as forecast inflation targeting since forward looking central banks should attempt to stabilize inflation expectations as a vehicle to affect future inflation. While IT involves the adoption of a set of policy rules, they still provide authorities with a significant degree of discretion. Against the rigid theoretical argument that places no weight on output deviations and no supply side shocks, Bernanke and Mishkin (1997) offer a more flexible alternative, where the output gap also enters the central bank welfare function and thus becomes a monetary objective. They cite New Zealand as being the most rigid IT central bank. Yet, despite this, the central bank's threepercentage point range does offer a level of discretion. Svensson (2000) compares strict and flexible inflation targeting in an open-economy model. In his model, the strict regime states that the central bank’s loss-function only weighs the deviations of inflation from target while no weight is placed on growth or exchange rate variance. On the other hand,   7     the monetary reaction function for flexible IT does place weight on all variables. Svensson concludes that a flexible IT monetary response results in lower variability of inflation, growth and real exchange rates. Instead, Woglom (2003) suggests that even a strict inflation targeter would weigh output variations as this feeds into future inflation through Phillips curve effects. Blanchard (2006) argues that, under fairly plausible conditions, there is a “Divine Coincidence” that results in a minimization of output and inflation volatility when a central bank targets inflation as its sole objective. He points out that a strict IT central bank that succeeds in stabilizing inflation will automatically generate the optimal level of activity. Blanchard’s results hold even in the presence of supply shocks. However, when in the presence of real wage rigidities, a strict IT regime may prove to be sub-optimal as it may be necessary to allow for higher inflation to reduce the output gap. Another dispute relates to whether IT central banks should react to exchange rate movements or not. Ball (1998) argues that the exchange rate may enhance the transmission mechanisms of monetary policy so it should be included (he actually suggests a monetary conditions index, which is a different instrument combining the policy rate and exchange rate). However, Edwards (2006) explains that there is no need since exchange rate effects are fully captured by the output gap and inflation deviations. Woodford (1999) addresses a different dimension of the problem of monetary policy implementation. He argues that an optimal policy rule for setting interest rates ought to involve a degree of gradualism. Indeed, while the shocks may be sizable and call for an ultimately large movement in interest rates, Woodford argues that central banks   8     will typically respond with significant (and oftentimes optimal) inertia in their interest rate setting. The point he makes is that since output and inflation respond to longer term interest rates and these, in turn, are linked to expectations of future interest rates, a credible signal of what the future path of interest rates will be is likely to yield a more effective movement in those long rates. In other words, Woodford argues that optimal policies require changes in the path of interest rates rather than actual, cold-turkey, large movements in short term rates. Woodford’s theoretical considerations extend the general arguments for interest rate smoothing that relied on model uncertainty or imperfect information as reviewed by Clarida, Gali and Gertler (1999). These theoretical arguments support much of the current rules used to implement IT around the world. Uncertainty can also have a meaningful impact on the way an IT regime is implemented. For instance, the response to an increase in uncertainty is very dependent on the characteristics of where the uncertainty emerges. Srour (1999) develops a simple linear-quadratic model to analyze uncertainty about different aspects of the economy.1 He shows that given the structure of his model, increases in the volatility of additive shocks should have no implications on the way policy is supposed to be formulated. However, uncertainty about how the economy will respond to a shock (the structure of parameters of the economy or multiplicative uncertainty) will typically lead to a more “cautious” stance –which is not the same as a slower response as it requires more aggressive interest rate hikes when uncertainty is about how inflation responds to policy shocks. Similarly, uncertainty about the lag structure with which policies will affect output and inflation, and uncertainty about whether a movement in output emerges from a shock or an                                                                                                                 1  See Gabriel Srour: Inflation targeting under uncertainty. Research Department, Bank of Canada. Technical Report No. 85. April 1999.     9     unknown lag structure for a policy, should typically lead policy makers to a partial adjustment. Finally, uncertainty over whether a shock is permanent or transitory ought to lead policy makers to undertake partial adjustments as they are discovering the duration of the actual disturbance. 3 Modeling a Reaction Function 3.1 A very basic model The empirical structure that we consider in this paper can be derived from three basic neo-Keynesian equations that describe an open economy. In developing these equations we consider elements from Ball (1998), Svensson (2000) and Clarida, Gali and Gertler (2000) to lay down a dynamic structural macroeconomic model that can define certain relations within the economy. Calling y the output gap; π inflation rate; and e the nominal exchange rate, we can model their relation as follows: (1) ! 𝑦! = −𝛽 𝑖!!! − 𝜋!!! − 𝛿 𝑒!!! + 𝜇 𝑦!!! + 𝜀!!" (2) ! 𝜋! = 𝛾 𝜋!!! −   1 − 𝛾 𝜋!!! + +𝜑   𝑦! + 𝜀!!" (3) 𝑒! = 𝜃 𝑖! + 𝑣 Equation (1) describes a dynamic open-economy IS equation, where output gap depends on lags of the nominal interest rate and exchange rate, a lag of itself, and an error term to capture demand shocks. Equation (2) is an open economy expectationsaugmented Phillips curve relating inflation to expectations, past inflation, current output gap, and supply shocks. Finally, equation (3) shows the relationship between the nominal   10     interest rate and the exchange rate. The idea is that an increase in the interest rate turns domestic assets more attractive leading to an appreciation of the currency. Ball describes this simplified relation, though he uses real variables instead. This should not have meaningful implications for our work, however, due to our assumption of price rigidities, especially if the model is empirically implemented at high frequencies. As in Ball (1998), a key component of the model is that policy affects inflation through two main channels. On the one hand, a depreciation of the exchange rate will pass through to domestic prices directly increasing inflation. On the other hand, lagged output will also affect inflation through Phillips curve effects (see Woglom, 2003). We also suggest a third channel that operates with longer lags. Shocks to exchange rates, when they generate expected inflation deviations from the target, may impact confidence on the central bank and could also have an effect on inflation. To derive a policy reaction function, we must first define a loss function. We assume that central banks minimize the following linear-quadratic loss function:2 (4) 𝐿 = 𝑉𝑎𝑟   𝜋 + 𝜆  𝑉𝑎𝑟 𝑦 , Where  λ is the weight assigned to output relative to inflation variation. Clearly, this loss function assumes symmetric weighing of negative and positive deviations which, in practice, may not be the case. The reduced-form solution is the policy reaction function: (5) 𝑖! = 𝑖! ∗ + 𝛼(𝜋!! − 𝜋!! ) + 𝛽  (𝑦! − 𝑦! ) + 𝜔  (𝑒! ) + 𝜀! !"                                                                                                                 2 This is a 1-period loss function, but could be extended to a multiple period one without loss of generality (Svensson (2003))     11     Where, (6) 𝑖! ∗ = 𝑟!∗ +  𝜋!! Here, r* is the neutral or equilibrium real interest rate that would prevail in the steady state when 𝜋!! =  𝜋!! and 𝑦! =  𝑦!∗ . Moreover, equation (6) yields a theoretical improvement from the original and many other Taylor rules specifications: the neutral nominal interest rate depends on the inflation target, not inflation or expected inflation. This is a significant distinction since in our model an increase in inflation met by an equal and instantaneous increase in the target would not lead to a movement in the policy instrument. Finally, most of the previous empirical literature estimating reaction functions assumes r* to be constant; however, as we will develop in Section 3.2, our empirical implementation will allow for a non-constant neutral real rate. Accordingly, to further ease interpretation of the policy rule, we modify the dependent variable to be as follows: (7) 𝑅! = 𝑖! − 𝑖!∗ Following the methods of Clarida, Gali and Gertler (2000) and the theoretical premises of Woodford (1999), we also add a lagged policy rule variable to the right-hand side of the reaction function to allow for smoothing, or inertia, in the policy rule. (8) 𝑅! = 𝜌𝑅!!! + 1 − 𝜌 [𝛼  (𝜋 ! − 𝜋 ! )!!! + 𝛽  (𝑦 − 𝑦)!!! + 𝜔(𝑒!!! )] + 𝜀!!" On a final note, in equation (8) we included lag operators for each of the explanatory variables to account for information lags that, typically, will be faced by policymakers. In   12     this case, the number of lagged periods is influenced by the publication delay of the variables for each country. 3.2 Data and Methods of Measurement 3.2.1 Data Most of the data was obtained from the respective central banks’ online databases. We estimated both our reduced form reaction function and structural vector autoregressive models with monthly data for the period of Full-Fledged or steady state IT for each country, which we will discuss in 3.2.2. The nominal interest rate is set equal to the objective policy rate in each country. The exchange rate change is computed as the monthly (end of period) percentage change in the nominal exchange rate. For simplicity, we adopt the convention that an appreciation of the currency equals an increase in the exchange rate. The output gap was calculated by taking the log ratio of output to potential GDP. For potential output we use a Hodrick-Prescott (HP) filter (𝜆 = 14400 as recommended for monthly data) to obtain a time-varying trend. Inflation is measured as the Consumer Price Index headline inflation. For expected inflation we used the central bank’s survey of 12-month ahead forecasts of market analysts in each country. Since Chile only provides data on expected inflation since 2003, we complete the series following a strategy from Aguirre and SchmidtHebbel (2005) by regressing survey inflation expectations on inflation expectations implicit in interest rate differentials and the inflation target. Then, we extrapolate the data back using the predicted fitted values.   13     3.2.2 Potential Problems with Non-Stationarity     The estimation of reaction functions in emerging countries faces a number of challenges. First, unlike in industrialized countries, the policy rules are usually adopted as a framework to stabilize and lower higher-than-target inflation rates. This implies that in many cases there is a long and challenging transition phase that is common under most regime changes. Second, as those central banks gain credibility, they tend to change the inflation targets and, more importantly, the “neutral real interest rate” also changes. The problem of somewhat prolonged transition phases oftentimes implies that policy responses will be different during the transition period from those in place in the steady state. As a result, empirical estimates conducted throughout the period of implementation of IT are likely to mix both regimes and yield unstable parameters. In particular, during periods of transition, central banks tend to change the nature of policy instruments. In the case of Mexico, the central bank formally adopted IT in 2001 using as its instrument the “corto” and, once inflation had been brought down from almost 23% to 4% in 2003, it began a convergence to an eventual steady-state adoption of the overnight policy rate as instrument. The instability in instruments, rules and large changes in inflation rates suggest that we need to be particularly careful not to mix openly transitional periods with steady state ones in our estimation. On the other hand, the need to have a significant number of business cycles requires us to have as extended a period of time as possible. For this reason, we choose to use the longest possible periods when inflation, policy rates and output appear to be near a steady state period. Our choice of sample periods attempts to address the mentioned trade-off. In the case of Chile, the central bank introduced in August 2001 a fundamental change in its   14     monetary instrument by switching from setting a real interest rate to adopting an overnight nominal policy rate. The transition between rates was conducted in a month when the real rate did not change from one month to the next and when the real rate plus the indexation unit (UF) equaled the 6.5% nominal rate set by the authorities. The authorities chose to introduce the change at a relatively stable time. However, a few months later, in December 2001, the central bank began a period of nominal rate cuts. As a result, we chose to define Chile’s steady state for IT as originating in August 2001. In Mexico, as suggested in our previous example, we chose to initiate our steady state sample in April 2004, at the time when the Central Bank of Mexico transitioned away from the use of the “corto” (in fact, only in February 2005 Mexico fully abandoned the use of the “corto”). Nominal interest rates between 2003 and 2005 were volatile, though they appear to fluctuate around a consistent trend. We expect this to have a minimal impact on the sign and size of the parameter estimates. The fundamental advantage is that we gain a full business cycle, which helps sharpen the estimation. Finally, in Brazil, despite the inflation targeting scheme being in place since 1999 (adopted at a time of high economic instability) the first signs of stability and relatively stable implementation of the policy regime took place in 2001. For this reason, we have chosen to begin our estimation in March 2001. We chose to initiate our analysis at that juncture despite the fact that Brazil’s political and economic crisis of 2002 tested the IT regime. However, the in-coming President decided to preserve the board composition (except for the governor) and they were mandated to implement the same policy framework as in the previous administration.   15     3.2.3 Time-varying neutral real interest rates It is always a challenge to assume constant neutral real interest rates, even in developed economies; it is even more so in emerging economies. In the latter countries, central banks usually gain credibility over time which, in turn, affects the risk premia associated with neutral real rates; furthermore, these are usually more open economies and, therefore, external factors that change long term external rates may also affect neutral rates. These potential movements in long term real rates result in meaningful trends, which could induce non-stationarity in the dependent variable. To be sure, the policy rate in our countries is non-stationary. Econometric estimation of Augmented Dickey Fuller tests show that in Chile, Brazil and Mexico, we cannot reject the hypothesis of a unit root. We hypothesize that the non-stationarity in neutral real rates emerges from a gradual consolidation of central bank credibility and a reduction in inflation risk premia, as well as a downward trend in long term –neutralforeign real interest rates.3 To construct time varying neutral real interest rates, we first define real interest rates as the policy rate minus the twelve-month forward expected inflation as measured in central bank surveys (𝑟!   =   𝑖!   −   𝜋!! ). Ultimately, we approximate the time-varying neutral real interest rates by applying a Hodrick-Prescott filter (HP) to our measure of real interest rates. However, this filter provides a non-economic procedure to capture smooth long term movements in a variable. To make sure that low frequency changes in                                                                                                                 3  There are other potential variables that might explain changes in neutral real rates, such as sovereign risk premia (the higher the risk of default, the higher the risk premia), indicators of fiscal policy stance (the higher the full-employment deficit, the higher the neutral real rate is likely to be), and other measures that might affect the long term aggregate demand of an economy. In the empirical estimates that follow, those variables tended to provide no additional explanatory value.       16     real interest rates are explained by fundamental economic variables, we conducted a cointegration analysis between real interest rates and our candidate economic variables. We approximate inflation risk through the absolute value of the difference between ex-post inflation and expected inflation: Abs[ 𝜋 ! !!!"  –  𝜋! ]. 4 The economic reasoning behind this proxy is that when inflation surprises are consistently increasing, in absolute value, inflation risk premia is likely to increase. Figure 1 illustrates the pattern of movement of inflation risk for our three countries. The credibility of a central bank is approximated by the distance between 12month ahead expected inflation and the inflation target. The economic justification is that when central banks are very credible, inflation expectations for the policy horizon ought to quickly revert to target. If inflation expectations remain consistently above (or below) the target, then the credibility of the current IT framework is in question. Our final variable considers the international neutral real rate. Here we assume that long term real rates can be estimated by the real interest rate that is expected to prevail in US inflation-linked bonds beyond the usual business-cycle horizon. One way to estimate such a variable is to compute the 5-year real rate that will be in place 5-years from now: the 5y5y forward real interest rate. We use US-TIPS (Treasury Inflation Protected Securities) to estimate this series.                                                                                                                 4  This is an approximation to an ARCH estimation of the standard deviation of unanticipated inflation (Robert Engle: GARCH 101: the Use of ARCH/GARCH Models in Applied Econometrics. Journal of Economic Perspectives – Volume 15, Number 4 – Fall 2001 – Pages 157-168).     17     Figure 1 – Inflation Premia by country Inflation Premia (Brazil) Inflation Premia (Chile) 7 14 6 12 5 10 4 8 3 6 2 4 1 2 0 0 01 02 03 04 05 06 07 08 09 10 01 11 02 03 04 05 06 07 08 09 10 11 Inflation Premia (Mexico) 3.6 3.2 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 01 02 03 04 05 06 07 08 09 10 11 Our next step is to test whether there is cointegration between the countries’ real interest rates and the explanatory variables. We use Johansen’s Cointegration test and the results are illustrated in Table 1. There, we find that in Brazil and Chile there is at least one cointegrating vector, while in Mexico we reject cointegration. The trace and maximum eigenvalue tests provide consistent results (showing that Brazil has one cointegrating vector while Chile has two). For the cases where there is cointegration, we then estimate first-stage cointegrating regressions, following Engle and Granger’s two stage procedure. When cointegration is present, such a regression is an indication of the long-term relationship between the variables and thus shed light on factors that affect the neutral real interest rate.   18     Table 1 - Cointegration test of long term real rates and economic variables Chile Brazil Variable 8/01-12/11 1/01-12/12 (1) (3) Johansen Trace - # of coint vectors Trace Statistic (5% critical value) Johansen Eigenval - # of coint vectors Max-Eingen Statistic (5% critical value) Engle-Granger First Stage Coint Regression Dependent variable: Real Interest Rate Central Bank Credibility: HP ( 𝜋 ! !  –  𝜋 ! t) Inflation Risk Premia: HP {Abs[𝜋 ! !!!"  –  𝜋! ]} Neutral Real Rate USA HP {5y5y fwd TIPS} Constant adj R^2 Mexico 1/03-12/11 (2) 2 Vectors 42.088 (35.19) 2 Vectors 25.845 (22.3) 1 Vector 65.079 (54.079) 1 Vector 42.7 (28.588) No-Coint 45.753 (54.079) No-Coint 23.16 (28.588) 5.94 (0.23) -0.14 (0.05) -0.87 (0.12) 2.31 (0.34) 0.851 -0.25 (0.75) 0.833 (0.44) 2.36 (0.38) 2.00 (0.75) 0.431 - Note: std deviations in parenthesis for the First Stage regressions. We did not run the First Stage regression for Mexico since we did not find any cointegrating vectors. In Brazil, every coefficient has the right sign and is significant except for the proxy for central bank credibility, which is insignificant. In Figure 2 we see that the fitted values of the regression are fairly good descriptors of a trend. Interestingly, while the fitted values share the same trend and provide a strong fit for the trend in the first years of the sample, it does not do as well in the later months resulting in a failure of the ADF.   19     Figure 2 – Brazil Figure 3 - Chile 16 5 14 4 12 3 2 10 1 8 0 6 -1 4 00 01 02 03 04 05 06 07 08 09 10 -2 11 01 First-S tag e Fitte d Tren d HP-Filter of Real Inte rest Rate 02 03 04 05 06 07 08 09 10 11 First-S tag e Fitte d Tren d HP-Filter of Real Inte rest Rate In the case of Chile, the only coefficient with the expected sign is the proxy for central bank credibility; nevertheless, the fit on the real interest rate is quite strong. This means that the neutral real interest rate has too much volatility – as seen in Figure 3. Due to the fact that neither of these trends fit the data well enough to facilitate interpretation, we choose to use the HP-filtered observed real interest rate. As shown in Figure 3, this trend is fairly similar to the fitted trends so as to have strong economic support, but also fits the data well to pass the ADF test. The absence of cointegration in Mexico is disconcerting and suggests that further empirical work needs to be done to identify economic drivers for the declining real interest rates. We think that long term neutral rates are indeed slowly changing and, thus, find the HP filter is probably a solid approximation to neutral rates. We proceed to use policyrate deviations from the HP filtered real rate and from the inflation target as our theoryinspired measure of the cyclical policy rate set by policy makers. Once we test the resulting policy rate for stationarity, we find that we reject the presence of a unit-root in all three cases.   20