Online Appendix for Forecasting Inflation using Survey Expectations and Target Inflation: Evidence for Brazil and Turkey

Transcription

1 Online Appendix for Forecasting Inflation using Survey Expectations and Target Inflation: Evidence for Brazil and Turkey Sumru Altug 1,2 and Cem Çakmaklı 1,3 1 Department of Economics, Koç University 2 CEPR 3 Department of Quantitative Economics, University of Amsterdam March 17, 2015 Sumru Altug (saltug@ku.edu.tr), Cem Çakmaklı (ccakmakli@ku.edu.tr, C.Cakmakli@uva.nl., corresponding author)

2 A Introduction In this Appendix, we provide additional details on the estimation of the state space model using the Kalman filter/smoother approach. We illustrate this approach only for the case of Turkey. This augments our discussion in Section 2, which presents the state and measurement equations for the state space model and uses these equations to generate the model-based term structure of inflation expectations. This discussion is in Section B. We also present in-sample estimation results for three separate models that add to the discussion in the main text. These include the specification with changes in global inflation in the slope process for inflation explicitly treated in the text. For the sake of completeness, we also estimate a specification with the level of global inflation in the latent process describing the slope of observed inflation. Finally, to complement the case with interest rates and the IP gap in the measurement equation for inflation discussed in Section 5.2 of the text, we consider a specification that includes the nominal exchange rate in the measurement equation for inflation in a time-varying parameter model. The motivation for the last model arises from the phenomenon of exchange rate pass-through that appears to be an important determinant of inflation dynamics for emerging economies such as Brazil and Turkey. These results are in Section C. The remaining results in this Appendix pertain to a comparison of the cyclical behavior of the discrepancy between model-based expectations from target inflation in the model that includes interest rates and the IP gap and the basic state space model. While the model withinterest rates and theipgap is discussedmorefullyin thetext, hereweprovide additional details of the discrepancy measure not available in the text. This discussion is in Section D. B Statistical Inference The model can be nicely cast into a state-space framework and standard inference can be carried out using the Kalman filter/smoother coupled with quasi-newton optimization methods. Here we provide details for the model used for Turkey. Specifically, the state space model in a more compact form is as follows 1

3 y t = BX t +HS t +ǫ t ǫ t N(0,R) S t = FS t 1 +η t η t N(0,Q), ( ( ) where y t = π t, Et S [π t+2 ], Et S [π t+12 ], Et,A t+12]) T [π, X t = π t 1, π t and S t = (α t,µ t,γ t,δ 0,t,α t 1,γ t 1,...,γ t 12 ). The system matrices are (1) H = φ φ j=1 φj j=1 φj j=1 φj j=1 φj j=1 φj j=1 φj , σ η 2 α σ ηα,µ σ ηα,γ σ ηα,δ σ ηα,µ ση 2 µ σ ηµ,γ σ ηµ,δ σ σ ηα,γ σ ηµ,γ ση 2 γ σ ηγ,δ ε 2 σ ε,υ2 σ ε,υ12 σ ε,υ T Q = σ ηα,δ σ ηµ,δ σ ηγ,δ ση 2 σ ε,υ2 συ 2 2 σ υ2,υ 12 σ υ2,υ δ ,R = T σ ε,υ12 σ υ2,υ συ 2 12 σ υ12,υ T σ ε,υ T σ υ2,υ T σ υ 12,υ T σ2 υ. T , F = j=1, B = φj j= φj j=1 φj

4 For Brazil the model is identical except for the fact that we use only one-year ahead survey based inflation expectations. Using (1) we can employ the Kalman filter. The loglikelihood is a by-product of the Kalman filter and maximized for obtaining inference on model parameters. Once the parameters are estimated, the Kalman filter (smoother) can be employed to obtain filtered (smoothed) estimates of unobserved components. An important feature of our modeling approach is that it can also handle missing observations due to the low frequency nature of the annual inflation target. The state space framework treats these missing observations in a statistically optimal way. Specifically, let W be the selection matrix as the identity matrix with the last diagonal element taking the value zero when the target inflation is not observed and 1 when it is observed. Then standard Kalman filter/smoother can be conducted using the modified version of the system in (1) using ỹ t = Wy t, H = WH, B = WB and R = WRW. The estimation procedure of the state space models become a common practice, hence for further details about the estimation of these models, we refer to the textbook expositions such as (Harvey, 1990) and (Durbin and Koopman, 2012). C Models with Additional Variables As we discussed in the text, we noted that there may be common factors in the inflation processes of emerging economies arising from the behavior of global inflation. We conducted a specification search for inclusion of global inflation in our setting. We evaluated two models where global inflation is used, first, as a determinant of the level of inflation process, and second, in form of changes as a determinant of the slope of inflation process. The version where the change in the global inflation is used as a determinant of the slope process providethebest results. We discuss this case morefully in thetext. Inthis section, we provide some key details of the specifications with global inflation in the latent slope and level processes for inflation, respectively. 3

5 C.1 Global inflation in the slope of inflation Consider an augmented version of the model that allows for the first principal component of inflation rates for the OECD countries as a measure of global inflation to affect the basic state space model. In the first extension, the change in global inflation affects the latent process for the slope of the inflation process as µ t = λµ t 1 +(1 λ) π G t +η α,t, (2) with the rest of the equations in (2.1) for π t, α t, and γ t remaining unchanged. We also need to specify a law of motion for the global inflation process. We assume that global inflation evolves as a random walk. In this case, the model-based inflation expectations at horizon k reflect the impact of changes on global inflation as follows. E S t [π t+k ] = k j=1 φj π t + ( k k j=1 φj) α t + ( k j=1 (k+1 j)λj 1) µ t + ( k (k 1)k j=1 2 (k j)λ j) πt G k j=1 φj γ t +υ k,t, (3) with the rest of the components of the full state space representation in equation (2.3) considered in the text remaining unchanged. Notice that when λ = 1 the specification reduces to (2.3). C.2 Global inflation in the level of inflation Asanalternative tothespecificationinthetextwithchanges inglobal inflationintheslope of inflation, consider the following modified version of the local level model for modeling inflation dynamics together with global inflation. This model includes the level of global inflation directly in the level process for inflation, α t as α t = λα t 1 +(1 λ)π G t +η α,t. (4) To be able to predict future values of global inflation into account, we assume a random walk process for the evolution of global inflation. In this case, the model-based inflation 4

6 expectations at horizon k reflect the impact of changes on global inflation as follows. E S t [π t+k] = k j=1 φj π t + ( k j=1 (λj φ j ) ) α t + ( k k j=1 λj) π G t k j=1 φj γ t +υ k,t (5) with the rest of the components of the full state space representation in equation (2.3) considered in the text remaining unchanged. Notice that when λ = 1 the specification reduces to (2.3) directly. C.3 Findings Tables B.1-B.2 present the full-sample results for the estimation of the model with global inflation in the slope of inflation while Figures B.1-B.2 present the estimated latent components of inflation for Brazil and Turkey, respectively. A comparison of the in-sample results for both Brazil and Turkey to the initial results from the model with λ = 1 reveals that the results are qualitatively similar. The differences involve the a higher value for the autoregressive parameter φ in the model with global inflation for Brazil, which implies a higher persistence in inflation as well as some larger variances of the errors in the equations for survey expectations and the target inflation relative to the baseline model. A comparison of the in-sample results to the initial results of the standard model for Turkey reveals that the results are also qualitatively quite similar. The major difference between two models is the increase in the variance of the error term in the target inflation equation. Table B.3-B.4 and Figures B.3-B.4, respectively. These results show that there is very little difference in the estimated parameters of the implied time varying components for inflation when global inflation is added as an additional determinant into the level process for inflation. This occurs because the estimate of the parameter λ is not significantly different from one, and is basically echoes the findings reported in the text for the case with changes in global inflation included in the slope of inflation. Since the model reported here does not add substantially to the results generated in the text, we provide it only as an illustration of altering the assumptions regarding the role of global inflation. 5

7 C.4 Model with the exchange rate and its first lag in the measurement equation: Time-varying parameter (TVP) model In this section, we consider a modified version of the model where we use the current nominal exchange rate and its first lag as explanatory variables of inflation with timevarying parameters. See Arslaner et al. (2014) for a recent paper on Turkey indicating that the exchange rate pass-through effect takes place almost immediately using many specifications, thus confirming our structure of explanatory variables for analyzing the exchange rate pass-through effect. Now the inclusion of exchange rate has an effect through the implied form of model-based inflation predictions as follows: π t X t α t γ t = φ(π t 1 X t 1 α t 1 γ t 1 )+ε t (6) We should also take future values of exchange rate and its first lag into account. One option is to assume a random walk for both. Here, X t = (1,XR t,xr t 1 ) In this case, the model-based inflation expectations at horizon k reflect the impact of nominal exchange rates as follows. E S t [π t+k ] = k j=1 φj π t + ( k k j=1 φj) X t α t k j=1 φj γ t +υ k,t (7) with the rest of the components of the full state space representation in equation (2.3) considered in the text remaining unchanged. We display the parameter estimates of the model in Table B.5 and B.6 and the estimated states infigureb.5andb.6forbrazil andturkey respectively. From thefigureb.6 for Turkey regarding the time varying parameters of the exchange rate (top right panel) and its first lag (middle left panel), we observe that these parameters eventually converge to low values around zero where the convergence takes place around 2010 for the first lag of exchange rate while for the current exchange rate, the convergence is already achieved around These results indicate empirically that exchange rate pass-through effect diminishes over the course of the sample for Turkey. This is in line with the findings of Arslaner et al. (2014). When we consider the graph in the bottom left panel of Figure B.6, 6

8 we observe that the evolution of the discrepancy of model-based inflation expectations from target inflation do not exhibit a significant difference compared our initial modeling framework. For Brazil, the exchange rate pass-through effect seems to be more pronounced. From Figure B.5 regarding the time varying parameters of the exchange rate (top right panel) and its first lag (middle left panel), we observe that the first parameter is quite stable around values of -0.2 while the latter displays a more volatile behavior around 0.2 yielding a low total effect. Accordingly, there are no significant changes in the evolution of the discrepancy of model-based inflation expectations from target inflation. D Discrepancy between model-based expectations from target: The role of cyclical factors The estimation of the model with interest rates and the IP gap allow us to examine the impact of accounting for cyclical factors on the discrepancy between model-based inflation expectations from target inflation. Figure C.1 and C.2 show the implied discrepancy between the model-based inflation expectations and target inflation calculated from the basic state space model and the one that includes interest rates and the IP gap to proxy for the output gap at the monthly frequency for Brazil and Turkey, respectively. Figure C.1 shows that the differences between the two models is not too pronounced for Brazil. The model with interest rate and output gap implies a stronger departure from the zero line towards the positive direction for the period 2007 and 2009, when there is a sharp contraction in the economic activity for Brazil. However, the baseline model also displays these swings, albeit to a lesser extent. In the case of Turkey displayed in Figure C.2, the discrepancy measure generated by both models moves in similar ways but there are some noteworthy differences. Specifically, while the evolution of the discrepancy between target inflation and model-based inflation expectations is smooth around -2%, there are more cyclical fluctuations around this value compared to the case for Brazil. We note that the presence of a negative output gap and thus, a decline in economic activity during 2004 and 2006, is accompanied by a decrease in the discrepancy towards zero. On the other hand, 7

9 the discrepancy widens towards values of -4% around mid-2008 where Turkey experiences an increase in economic activity according to the output gap measure. Again, at the onset of the 2009 recession for Turkey which witnesses a large and sudden decrease in the policy rate, the discrepancy comes closer to zero. This pattern indicates the cyclicality of the discrepancy between model-based inflation expectations and target inflation such that the discrepancy approaches to zero during times of economic distress and widens during times of economic expansion. While this behavior is evident for both Turkey and Brazil, the distinction between the two models is much more pronounced for Turkey. 8

10 References Arslaner, F., D. Karaman, N. Arslaner, and S. H. Kal (2014), The Relationship between Inflation Targeting and Exchange Rate Pass-Through in Turkey with a Model Averaging Approach, Tech. rep. Durbin, J. and J. Koopman (2012), Time Series Analysis by State Space Methods: Second Edition, OUP Catalogue, Oxford University Press. Harvey, A. (1990), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge Books, Cambridge University Press. 9

11 Table B.1: Estimation results for Brazil: Global inflation in the slope of inflation φ σ 2 η α σ 2 η µ σ 2 η γ σ ηα,η µ σ ηα,η γ σ ηµ,η γ Estimate St. dev (0.031) (0.003) (0.000) (0.028) ( ) (0.015) (0.0002) ση 2 δ σ ηδ,η α σ ηδ,η µ σ ηδ,η γ λ Estimate St. dev (0.933) (0.055) (0.001) (0.252) (0.000) σε 2 συ 2 12 σ 2 υ T σ ε,υ12 σ ε,υ T σ υ12,υ T Estimate St. dev. (0.262) (05) (0.982) (0.332) (0.610) (0.653) Note: The table presents estimation results with standard deviations (in parentheses) of parameters of the model detailed in (3) using data on the CPI inflation rate for Turkey together with CBRT two-month and one-year ahead survey inflation expectations and the inflation target over the period from August 2001 to January Table B.2: Estimation results for Turkey: Global inflation in the slope of inflation φ σ 2 η α σ 2 η µ σ 2 η γ σ ηα,η µ σ ηα,η γ σ ηµ,η γ Estimate St. dev (0.033) (0.000) (0.000) (0.007) (0.0001) (0.0013) (0.0002) ση 2 δ σ ηδ,η α σ ηδ,η µ σ ηδ,η γ λ Estimate St. dev (0.011) (0.003) (0.0001) (0.016) σε 2 συ 2 2 συ 2 12 σ 2 υ T σ ε,υ2 σ ε,υ12 σ ε,υ T Estimate St. dev (0.052) (0.018) (0.040) (1.043) (0.031) (0.041) (0.292) σ υ2,υ 12 σ υ2,υ T σ υ 12,υ T Estimate St. dev (0.025) (0.052) (0.197) Note: Note: The table presents estimation results with standard deviations (in parentheses) of parameters of the state space model modified as in (3) using data on the CPI inflation rate obtained for Turkey, the CBRT two-month and one-year ahead survey inflation expectations, the inflation target and the global inflation rate over the period from August 2001 to January Table B.3: Estimation results for Brazil: Global inflation in the level of inflation φ σ 2 η α σ 2 η γ σ ηα,η γ Estimate St. dev (0.030) (0.004) (0.110) (0.020) ση 2 δ σ ηδ,η α σ ηδ,η γ λ Estimate St. dev (0.979) (0.063) (0.313) (0.000) σε 2 συ 2 12 σ 2 υ T σ ε,υ12 σ ε,υ T σ υ12,υ T Estimate St. dev. (0.270) (0.358) (0.627) (0.281) (0.436) (0.473) Note: The table presents estimation results with standard deviations (in parentheses) of parameters of the model detailed in (5) using CPI inflation for Brazil together with one-year ahead survey inflation expectations, the inflation target and global inflation over the period from August 2001 to January

12 Table B.4: Estimation results for Turkey: Global inflation in the level of inflation φ σ 2 η α σ 2 η γ σ ηα,η γ Estimate St. dev (0.050) (0.000) (0.006) (0.001) ση 2 δ σ ηδ,η α σ ηδ,η γ λ Estimate St. dev (0.007) (0.001) (0.010) (0.000) σε 2 συ 2 2 συ 2 12 σ 2 υ T σ ε,υ2 σ ε,υ12 σ ε,υ T Estimate St. dev (0.033) (0.038) (0.247) (0.314) (0.015) (0.021) (0.028) σ υ2,υ 12 σ υ2,υ T σ υ 12,υ T Estimate St. dev (0.032) (0.134) (47) Note: The table presents estimation results with standard deviations (in parentheses) of parameters of the model detailed in (5) using CPI inflation for Turkey together with CBRT two-month and one-year ahead survey inflation expectations, the inflation target and the global inflation rate over the period from August 2001 to January Table B.5: Estimation results for Brazil: Exchange rates in the measurement equation for inflation φ σ 2 η α1 σ 2 η α2 σ 2 η α3 σ ηα1,η α2 σ ηα1,η α3 σ ηα2,η α3 Estimate St. dev (0.026) (0.024) (0.007) (0.000) (0.003) (0.0001) (0.0057) ση 2 γ σ ηγ,ηα1 σ ηγ,ηα2 σ ηγ,ηα3 σ ηγ,ηδ Estimate St. dev (0.000) (0.0000) (0.0621) (0.0000) (0.1747) ση 2 δ σ ηδ,η α1 σ ηδ,η α2 σ ηδ,η α3 Estimate St. dev (0.001) (0.000) (0.000) (0.001) σε 2 συ 2 12 σ ε,υ2 σ ε,υ12 σ ε,υ T σ υ12,υ T Estimate St. dev (0.016) (1.839) (2.179) (0.119) (0.140) (1.906) Note: The table presents estimation results with standard deviations (in parentheses) of parameters of the model detailed in (7) using the inflation obtained from consumer price index in Brazil together with one-year ahead survey inflation expectations and the inflation target over the period from November 2001 to January

13 Table B.6: Estimation results for Turkey: Exchange rates in the measurement equation for inflation φ σ 2 η α1 σ 2 η α2 σ 2 η α3 σ ηα1,η α2 σ ηα1,η α3 σ ηα2,η α3 Estimate St. dev (0.018) (0.003) (0.0007) (0.0005) (0.0013) (0.0059) (0.0057) ση 2 γ σ ηγ,ηα1 σ ηγ,ηα2 σ ηγ,ηα3 σ ηγ,ηδ Estimate St. dev (0.002) (0.0016) (0.0032) (0.0000) (0.0122) ση 2 δ σ ηδ,η α1 σ ηδ,η α2 σ ηδ,η α3 Estimate St. dev (0.000) (0.003) (0.000) (0.012) σε 2 συ 2 2 συ 2 12 σ 2 υ T σ ε,υ2 σ ε,υ12 σ ε,υ T Estimate St. dev (0.034) (0.011) (0.027) (0.377) (0.018) (0.026) (0.345) σ υ2,υ 12 σ υ2,υ T σ υ 12,υ T Estimate St. dev (0.014) (0.015) (0.222) Note: The table presents estimation results with standard deviations (in parentheses) of parameters of the model detailed in (7) using the inflation obtained from consumer price index in Turkey together with CBRT two-month and one-year ahead survey inflation expectations and the inflation target over the period from August 2001 to January Figure B.1: Estimated Components of Inflation for Brazil: Global Inflation in the Slope of Inflation Note: The graphs show the inflation level, slope, and seasonality based on the full state space model modified as in (3) with global inflation in the slope of inflation together with Central Bank of Brazil survey expectations of one-year ahead inflation and the estimated deviations from target inflation for the period November 2001-January

14 Figure B.2: Estimated Components of Inflation for Turkey: Global Inflation in the Slope of Inflation 5 Smoothed Inflation Level Estimates 1.5 Smoothed Inflation Seasonality Estimates Smoothed Inflation Slope Estimates 0 Deviation of Inflation Expectations from Target Inflation Note: The graphs show the inflation level, slope, and seasonality based on the full state space model modified as in (3) with global inflation in the slope of inflation together with CBRT survey expectations of two-month and one-year ahead inflation and the estimated deviations from target inflation for the period August 2001-January

15 Figure B.3: Estimated Components of Inflation for Brazil: Global inflation in the level of inflation Note: The graphs show the expectations of monthly inflation and its level based on the model with global inflation in the level of inflation in (5) for the period November 2001-January 2014 for Brazil. 14

16 Figure B.4: Estimated Components of Inflation for Turkey: Global inflation in the level of inflation Note: The graphs show the inflation level, slope, and seasonality based on the full state space model in (5) with global inflation in the level of inflation together with CBRT survey expectations of two-month and one-year ahead inflation and the estimated deviations from target inflation for the period August 2001-January

17 Figure B.5: Estimated Components of Inflation for Brazil: Exchange rates in the measurement equation for inflation Note: Thegraphs showfrom left torightandfrom toptobottomtheevolutionoftimevaryingintercept, the coefficient of IP gap and interest rate, seasonality component and deviations of inflation expectations from target inflation in Turkey based on the model in (7) estimated using the period November 2001-January

18 Figure B.6: Estimated Components of Inflation for Turkey: Exchange rates in the measurement equation for inflation Note: The graphs show from left to right and from top to bottom the evolution of time varying intercept, the coefficient of IP gap and interest rate, seasonality component and deviations of inflation expectations from target inflation in Turkey based on the model in (7) estimated using the period August 2001-January

19 Figure C.1: Estimation results for Brazil Note: The graphs show the discrepancy between the model-based expectations and the target inflation for the basic model and for the model with interest rates and the IP gap for the period November 2001-January 2014 for Brazil. Figure C.2: Estimation results for Turkey Note: The graphs show the discrepancy between the model-based expectations and the target inflation for the basic model and for the model with interest rates and the IP gap for the period August 2001-January 2014 for Turkey. 18