Abstract
In this paper, we investigate the forecasting performance of the median Consumer Price Index (CPI) in a variety of Bayesian Vector Autoregressions (BVARs) that are often used for monetary policy. Until now, the use of trimmed-mean price statistics in forecasting inflation has often been relegated to simple univariate or “Phillips-Curve” approaches, thus limiting their usefulness in applications that require consistent forecasts of multiple macro-variables. We find that inclusion of an extreme trimmed-mean measure—the median CPI—improves the forecasts of both core and headline inflation (CPI and personal consumption expenditures price index) across our set of monthly and quarterly BVARs. While the inflation forecasting improvements are perhaps not surprising given the current literature on core inflation statistics, we also find that inclusion of the median CPI improves the forecasting accuracy of the central bank’s primary instrument for monetary policy—the federal funds rate. We conclude with a few illustrative exercises that highlight the usefulness of using the median CPI.
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Notes
See http://www.federalreserve.gov/monetarypolicy/fomccalendars.htm for more details.
We are aware that the FOMC has chosen to target PCE inflation. For purposes of this paper, we are making the switch back to the CPI. We leave the construction and evaluation of a median PCE for further research, but given that roughly ¾ of the initial PCE release is constructed directly from CPI component indexes, we doubt that the results will differ qualitatively.
In contrast, Giannone and Matheson (2007) using CPI data for New Zealand show that trimmed-mean estimators including the median CPI were unable to outperform the method that utilized dynamic factor model and disaggregated CPI data in predicting future inflation. Specifically, they were trying to predict the target inflation which they defined as the centred two-year moving average of the past and future inflation.
We ran a few forecasting tests using the 16% trimmed-mean CPI and, consistent with Meyer and Venkatu (2012) found qualitatively similar results.
In light of recent research (e.g. Gamber et al. (2015)) documenting an existence of a dynamic relationship between median CPI inflation and headline CPI inflation that is stable across monetary regimes we also ran model specifications that included information about the deviation of headline inflation from the median CPI (i.e. gap between the two) in addition to the median CPI. The results were quantitatively very similar. In the interest of brevity, we do not report those results.
For these, we report forecast evaluation results that are “static” in nature. That is our last estimation run stops in 2005:Q3 giving us same number of one-step to eight-step forecast errors over the forecast evaluation window.
We take 1000 draws of VAR coefficient matrix A, and error variance and covariance matrix \( \sum \) to compute the predictive density.
We also assess the accuracy of density forecasts using another widely employed metric log-score. The results are robust to using either CRPS or log-score. We report results using CRPS due to our preference for this metric; it is easier to interpret as forecast error metric. Results corresponding to the log-score are available on request from the authors.
We make an adjustment to correct the standard errors for heteroskedasticity and autocorrelation using the Newey–West estimator. Using pre-whitened quadratic spectral kernel introduced by Andrews and Monahan (1992) gives very similar results.
We also perform this forecasting exercise in a classical VAR framework (or a BVAR with very diffuse priors). The results are qualitatively similar to those we report.
Detailed tables for each model appear in Online Appendix A1.
Our implementation uses the MATLAB code corresponding to the BGR paper shared by Domenico Giannone on his website.
Due to data availability, our sample starts in January 1971.
In the baseline set-up, Carriero et al. (2015) use hyperparameter values λ = 0.2, µ = 1, and τ = 1. Our forecasting results are very similar if we instead use those values.
At least so far this is the case in the USA.
The eight-step-ahead forecast generated at the forecast origin 2005:Q3 corresponds to forecast date of 2007:Q3. The forecast evaluation results one-step- to eight-step-ahead reported for fed funds rate are static in nature. That is, the same number of one-step- to eight-step-ahead forecasts errors is used in computing the squared errors. We have also performed the forecast evaluation using the unconditional forecasting throughout the recursive sample (i.e. without conditional forecasting). The results are qualitatively similar for all variables except the fed funds rate, in which the forecasts from models that include the median CPI dramatically improve upon models without the median CPI, but are still, in an absolute sense, very poor. These unconditional results are available on request.
Some policymakers may balk at this suggestion, stating that communicating the change to the public would be difficult. However, in the early 2000s, despite widespread awareness of the CPI, the Committee switched to implicitly targeting PCE-based inflation. Moreover, in times when food and energy prices are spiking (such as mid-2008 or 2011), public outbursts arise decrying the central bank’s ignoring of these price changes. (see http://online.wsj.com/article/SB10001424052748704893604576199113452719274.html for an example).
We thank Domenico Giannone for suggesting this exercise.
A contractionary monetary policy shock leads to increase in prices which are contrary to intuition, but this result is expected because significant body of research (dealing with monetary VARs) has documented this behaviour and accordingly dubbed it the “price puzzle”.
References
Andrews DW, Monahan J (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60(4):953–966
Ball L, Mazumder S (2011) Inflation dynamics and the great recession. International monetary fund working paper, WP/11/121
Banbura M, Giannone D, Reichlin L (2010) Large Bayesian vector auto regressions. J Appl Econom 25(1):71–92
Beauchemin K, Zaman S (2011) A medium scale forecasting model for monetary policy. Federal Reserve Bank of Cleveland Working Paper 11–28
Bryan MF, Cecchetti SG (1994) Measuring core inflation. In: Gregory Mankiw EN (ed) Monetary Policy. University of Chicago Press, Chicago, pp 195–215
Bryan MF, Pike CJ (1991) Median price changes: an alternative approach to measuring current monetary inflation. Federal Reserve Bank of Cleveland, Economic Commentary 12.01.1991
Bryan MF, Cecchetti SG, Wiggins RL (1997) Efficient Inflation Estimation. National Bureau of Economic Research Working Paper no. 6183
Carriero A, Clark TE, Marcellino M (2015) Bayesian VARs: specification choices and forecast accuracy. J Appl Econom 30(1):46–73
Christiano LJ, Eichenbaum M, Evans CL (1999) Monetary policy shocks: what have we learned and to what end? In: Taylor JB, Woodford M (eds) Handbook of macroeconomics, vol 1. Elsevier, New York, pp 65–148
Clark TE (2001) Comparing measures of core inflation. Fed Reserve Bank Kansas City Econ Rev 86:5
Clark TE, McCracken MW (2013a) Advances in Forecast Evaluation. In: Elliott G, Timmermann A (eds) Handbook of economic forecasting, vol 2. Elsevier, New York, pp 1107–1201
Clark TE, McCracken MW (2013b) Tests of equal forecast accuracy for overlapping models. J Appl Econom 29(3):415–430
Crone TM, Khettry NK, Mester LJ, Novak JA (2013) Core measures of inflation as predictors of total inflation. J Money Credit Bank 45:505–519
Detmeister AK (2011) The usefulness of Core PCE inflation measures. federal reserve board finance and economics discussion series working papers no: 2011-56
Diebold FX, Mariano RS (1995) Comparing Predictive Accuracy. J. Business Econ Stat 13(3):253–263
Doan T, Litterman R, Sims C (1984) Forecasting and conditional projection using realistic prior distributions. Econom Rev 3:1–100
Dolmas J (2005) Trimmed mean PCE inflation. Federal Reserve Bank of Dallas, Research Department Working Paper 0506
Gamber EN, Smith JK, Eftimoiu R (2015) The dynamic relationship between core and headline inflation. J Econ Business 81:38–53
Giannone D, Matheson TD (2007) A New Core Inflation Indicator for New Zealand. Int J Central Bank 3:145
Gneiting T, Raftery A (2007) Strictly proper scoring rules, prediction and estimation. J Am Stat Soc 102(477):359–378
Kadiyala KR, Karlsson S (1997) Numerical methods for estimation and inference in Bayesian VAR-Models. J Appl Econom 12(2):99–132
Litterman R (1986) Forecasting with Bayesian Vector autoregressions-five years of experience. J Business Econom Stat 4:25–38
Meyer BH, Pasaogullari M (2010) Simple ways to forecast inflation: what works best? Federal Reserve Bank of Cleveland, Economic Commentary, No. 2010-17
Meyer BH, Venkatu G (2012) Trimmed-mean inflation statistics: just hit the one in the middle. Federal Reserve Bank of Cleveland Working Paper 12–17
Norman D, Richards A (2012) The forecasting performance of single equation models of inflation. Econom Rec 88(280):64–78
Sims, C. A. (1992) Bayesian Inference for Multivariate Time Series with Trend. Presentation at the 1992 American Statistical Association meetings
Sims C, Zha T (1998) Bayesian methods fro dynamic multivariate models. Int Econ Rev 39(4):949–968
Smith JK (2004) Weighted median inflation: is this core inflation. J Money Credit Bank 36:253–263
Stock JH, Watson MW (2005) An empirical comparison of methods for forecasting using many predictors. Manuscript, Princeton University
Stock JH, Watson MW (2008) Phillips curve inflation forecasts. NBER working papers 14322
Tallman EW, Zaman S (2012) Where would the federal funds rate be, if it could be negative?. Federal Reserve Bank of Cleveland Economic Commentary, No. 2012-15
Waggoner DF, Zha T (1999) Conditional forecasts in dynamic multivariate models. Rev Econ Stat 81(4):639–651
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The views expressed herein are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Atlanta, Federal Reserve Bank of Cleveland, or the Federal Reserve System. Brent Meyer thankfully acknowledges that much of the research documented in this paper was performed while he was a member of the Research Department at the Cleveland Fed. The authors thank the Editor, Robert KUNST, and also the anonymous associate editor and referees for helpful comments. We also thank Todd Clark, Domenico Giannone, Edward Knotek II, Ellis Tallman, and Randy Verbrugge for their helpful criticisms and guidance. They also thank conference participants at the 35th International Symposium on Forecasting in Riverside, California.
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Meyer, B., Zaman, S. The usefulness of the median CPI in Bayesian VARs used for macroeconomic forecasting and policy. Empir Econ 57, 603–630 (2019). https://doi.org/10.1007/s00181-018-1472-1
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DOI: https://doi.org/10.1007/s00181-018-1472-1