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Detecting time variation in the price puzzle: a less informative prior choice for time varying parameter VAR models

  • Peter Reusens EMAIL logo and Christophe Croux
Published/Copyright: September 4, 2017
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Studies in Nonlinear Dynamics & Econometrics
From the journal Studies in Nonlinear Dynamics & Econometrics Volume 21 Issue 4

Abstract

This paper compares Bayesian estimators with different prior choices for the time variation of the coefficients of Time Varying Parameter Vector Autoregression models using Monte Carlo simulations. Since the commonly used prior choice only allows for a tiny amount of time variation, less informative priors are proposed. Additional empirical evidence on the time varying response of inflation to an interest rate shock is provided for USA. While a ‘price puzzle’ is detected for the period 1972–1979, the estimated response of inflation to an interest rate shock is negative for most other time periods.

Keywords: inverse Wishart prior; Monte Carlo simulation; price puzzle; time varying parameter; vector autoregression

Acknowledgments

We are thankful to Geert Dhaene, Gerdie Everaert, Michele Lenza, Karel Mertens, Gert Peersman, Frank Smets and Joris Wauters for useful discussions and helpful comments. Also, financial support from the Agency for Innovation by Science and Technology in Flanders (IWT) is gratefully acknowledged.

A Appendix

Overview of the empirical literature

Figure 9: Estimated parameters reported in the macroeconomic literature for the ‘local level model’ (above the dashed line) and for more complex univariate models (below the dashed line). Each row represents a study and each column shows summary information. When necessary, we have translated the values of Q and Σ to correspond to annualized percentage growth rates. NA means that the information is not available in the paper. When a range of values is given, the results are for multiple variables or for multiple estimators.
Figure 9:

Estimated parameters reported in the macroeconomic literature for the ‘local level model’ (above the dashed line) and for more complex univariate models (below the dashed line). Each row represents a study and each column shows summary information. When necessary, we have translated the values of Q and Σ to correspond to annualized percentage growth rates. NA means that the information is not available in the paper. When a range of values is given, the results are for multiple variables or for multiple estimators.

B Appendix

Boxplot of the estimated amount of time variation of the local level model

Figure 10: Each subfigure corresponds to one simulation design and shows the boxplot of the estimated Q of the local level model over the 200 simulation runs. The horizontal axis represents the different estimators which are labeled 1 (df = 0.00001, scale = 0.00001), 2 (df = 0.1, kQ = 0.01), 3 (df = 2, kQ = 0.01), 4 (df = 20, kQ = 0.01), 5 (the Bayesian estimator with Gaussian prior) and 6 (the maximum likelihood estimator). Finally, the horizontal line is the true Q value of the data generating process.
Figure 10:

Each subfigure corresponds to one simulation design and shows the boxplot of the estimated Q of the local level model over the 200 simulation runs. The horizontal axis represents the different estimators which are labeled 1 (df = 0.00001, scale = 0.00001), 2 (df = 0.1, kQ = 0.01), 3 (df = 2, kQ = 0.01), 4 (df = 20, kQ = 0.01), 5 (the Bayesian estimator with Gaussian prior) and 6 (the maximum likelihood estimator). Finally, the horizontal line is the true Q value of the data generating process.

References

Aguiar, A., and M.Martins. 2005. “Testing the Significance and the Non-linearity of the Phillips Trade-Off in the Euro Area.” Empirical Economics30: 665–691.10.1007/s00181-005-0250-zSearch in Google Scholar

Amir-Ahmadi, P., C.Matthes, and M.-C.Wang. 2016. “Choosing Prior Hyperparameters.”Working Paper 16-9. Federal Reserve Bank of Richmond. URL https://ideas.repec.org/p/fip/fedrwp/16-09.html.Search in Google Scholar

Barth, M. J., and V. A.Ramey. 2002. “The Cost Channel of Monetary Transmission.” NBER Macroeconomics Annual16: 199–256.10.3386/w7675Search in Google Scholar

Baumeister, C., P.Liu, and H.Mumtaz. 2010. “Changes in the Transmission of Monetary Policy: Evidence from a Time Varying Factor-Augmented VAR.”Bank of England working papers 401, Bank of England. URL http://ideas.repec.org/p/boe/boeewp/0401.html.10.2139/ssrn.1701142Search in Google Scholar

Baumeister, C., and G.Peersman. 2013. “Time-Varying Effects of Oil Supply Shocks on the US Economy.” American Economic Journal: Macroeconomics5: 1–28.10.1257/mac.5.4.1Search in Google Scholar

Belaygorod, A., and M.Dueker. 2009. “Indeterminacy, Change Points and the Price Puzzle in an Estimated DSGE Model.” Journal of Economic Dynamics and Control33: 624–648.10.1016/j.jedc.2008.08.009Search in Google Scholar

Belmonte, M. A. G., G.Koop, and D.Korobilis. 2013. “Hierarchical Shrinkage in Time-Varying Parameter Models.” Journal of Forecasting33: 80–94.10.1002/for.2276Search in Google Scholar

Boivin, J., and M. P.Giannoni. 2006. “Has Monetary Policy Become More Effective?” The Review of Economics and Statistics88: 445–462.10.3386/w9459Search in Google Scholar

Carlstrom, C. T., T. S.Fuerst, and M.Paustian. 2009. “Monetary Policy Shocks Choleski Identification, and DNK Models.” Journal of Monetary Economics56: 1014–1021.10.1016/j.jmoneco.2009.09.009Search in Google Scholar

Carter, C. K., and R.Kohn. 1994. “On Gibbs Sampling for State Space Models.” Biometrika81: 541–553.10.1093/biomet/81.3.541Search in Google Scholar

Castelnuovo, E. 2012. “Testing the Structural Interpretation of the Price Puzzle with a Cost-Channel Model.” Oxford Bulletin of Economics and Statistics74: 425–452.10.1111/j.1468-0084.2011.00658.xSearch in Google Scholar

Castelnuovo, E., and P.Surico. 2010. “Monetary Policy, Inflation Expectations and the Price Puzzle.” Economic Journal120: 1262–1283.10.1111/j.1468-0297.2010.02368.xSearch in Google Scholar

Clarida, R., J.Gali, and M.Gertler. 2000. “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory.” The Quarterly Journal of Economics115: 147–180.10.3386/w6442Search in Google Scholar

Clark, T. E., and F.Ravazzolo. 2015. “The Macroeconomic Forecasting Performance of Autoregressive Models with Alternative Specifications of Time-Varying Volatility.” Journal of Applied Econometrics30 (4): 551–575.10.26509/frbc-wp-201218Search in Google Scholar

Cogley, T., and T. J.Sargent. 2001. “Evolving Post-World War II U.S. Inflation Dynamics.” NBER Macroeconomics Annual16: 331–388.10.1086/654451Search in Google Scholar

Cogley, T., and T. J.Sargent. 2005. “Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII US.” Review of Economic Dynamics8: 262–302.10.1016/j.red.2004.10.009Search in Google Scholar

Commandeur, J. J., and S. J.Koopman. 2007An Introduction to State Space Time Series AnalysisOxford: Oxford University Press.Search in Google Scholar

D’Agostino, A., L.Gambetti, and D.Giannone. 2013. “Macroeconomic Forecasting and Structural Change.” Journal of Applied Econometrics28: 82–101.10.1002/jae.1257Search in Google Scholar

Del Negro, M., and G. E.Primiceri. 2015. “Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum.” Review of Economic Studies82: 1342–1345.10.1093/restud/rdv024Search in Google Scholar

Demiralp, S., K.Hoover, and S.Perez. 2014. “Still Puzzling: Evaluating the Price Puzzle in an Empirically Identified Structural Vector Autoregression.” Empirical Economics46: 701–731.10.1007/s00181-013-0694-5Search in Google Scholar

Eichenbaum, M. 1992. “‘Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy’: By Christopher Sims.” European Economic Review36: 1001–1011.10.1016/0014-2921(92)90042-USearch in Google Scholar

Eisenstat, E., J.Chan, and R.Strachan. 2016. “Stochastic Model Specification Search for Time-Varying Parameter VARs.” Econometric Reviews35: 1638–1665.10.1080/07474938.2015.1092808Search in Google Scholar

Francis, N., and M. T.Owyang. 2005. “Monetary Policy in a Markov-Switching Vector Error-Correction Model.” Journal of Business and Economic Statistics23: 305–313.10.1198/073500104000000325Search in Google Scholar

Fruhwirth-Schnatter, S., and H.Wagner. 2010. “Stochastic Model Specification Search for Gaussian and Partial Non-Gaussian State Space Models.” Journal of Econometrics154: 85–100.10.1016/j.jeconom.2009.07.003Search in Google Scholar

Gelman, A. 2006. “Prior Distributions for Variance Parameters in Hierarchical Models.” Bayesian Analysis1: 1–19.10.1214/06-BA117ASearch in Google Scholar

Giordani, P. 2004. “An Alternative Explanation of the Price Puzzle.” Journal of Monetary Economics51: 1271–1296.10.1016/j.jmoneco.2003.09.006Search in Google Scholar

Hanson, M. S. 2004. “The ‘Price Puzzle’ Reconsidered.” Journal of Monetary Economics51: 1385–1413.10.1016/j.jmoneco.2003.12.006Search in Google Scholar

Harvey, A., and S.Koopman. 2009. “Unobserved Components Model in Economics and Finance: The Role of the Kalman Filter in Time Series Econometrics.” EEE Control System Magazine29: 71–81.Search in Google Scholar

Harvey, A. C., and A.Jaeger. 1993. “Detrending, Stylized Facts and the Business Cycle.” Journal of Applied Econometrics8: 231–247.10.1002/jae.3950080302Search in Google Scholar

Harvey, A. C., T. M.Trimbur, and H.Van Dijk. 2007. “Trends and Cycles in Economic Time Series: A Bayesian Approach.” Journal of Econometrics140: 618–649.10.1016/j.jeconom.2006.07.006Search in Google Scholar

Koop, G., and D.Korobilis. 2010. “Bayesian Multivariate Time Series Methods for Empirical Macroeconomics.” Foundations and Trends(R) in Econometrics3: 267–358.10.1561/0800000013Search in Google Scholar

Koop, G., and D.Korobilis. 2013. “Large Time-Varying Parameter VARs.” Journal of Econometrics177: 185–198.10.1016/j.jeconom.2013.04.007Search in Google Scholar

Koop, G., and S.Potter. 2004. “Forecasting in Dynamic Factor Models Using Bayesian Model Averaging.” Econometrics Journal7: 550–565.10.1111/j.1368-423X.2004.00143.xSearch in Google Scholar

Koop, G., and S. M.Potter. 2011. “Time Varying VARs with Inequality Restrictions.” Journal of Economic Dynamics and Control35: 1126–1138.10.1016/j.jedc.2011.02.001Search in Google Scholar

Korobilis, D. 2014. “Data-Based Priors for Vector Autoregressions with Drifting Coefficients.”MPRA Paper 53772. University Library of Munich, Germany. URL http://ideas.repec.org/p/pra/mprapa/53772.html.10.2139/ssrn.2392028Search in Google Scholar

Lubik, T. A., C.Matthes, and A.Owens. 2016. “Beveridge Curve Shifts and Time-Varying Parameter VARs.” Economic Quarterly102: 197–223.10.21144/eq1020302Search in Google Scholar

Lubik, T. A., and F.Schorfheide. 2004. “Testing for Indeterminacy: An Application to U.S. Monetary Policy.” American Economic Review94: 190–217.10.1257/000282804322970760Search in Google Scholar

Muirhead, R. 1982Aspects of Multivariate Statistical TheoryHoboken, NJ: Wiley.10.1002/9780470316559Search in Google Scholar

Mumtaz, H., and L.Sunder-Plassmann. 2013. “Time Varying Dynamics of the Real Exchange Rate: An Empirical Analysis.” Journal of Applied Econometrics28: 498–525.10.1002/jae.2270Search in Google Scholar

Nakajima, J. 2011. “Time-Varying Parameter VAR Model with Stochastic Volaitlity: An Overview of Methodology and Empirical Applications.” Monetary and Economics Studies29: 107–142.Search in Google Scholar

Petris, G. 2010. “An R Package for Dynamic Linear Models.” Journal of Statistical Software36: 1–16. URL http://ideas.repec.org/a/jss/jstsof/36i12.html.10.18637/jss.v036.i12Search in Google Scholar

Primiceri, G. E. 2005. “Time Varying Structural Vector Autoregressions and Monetary Policy.” Review of Economic Studies72: 821–852.10.1111/j.1467-937X.2005.00353.xSearch in Google Scholar

Rabanal, P. 2003. “The Cost Channel of Monetary Policy.”IMF Working Papers 03/149. URL http://ideas.repec.org/p/imf/imfwpa/03-149.html.10.5089/9781451856910.001Search in Google Scholar

Rossi, P. E., G. M.Allenby, and R.McCulloch. 2005Bayesian Statistics and Marketing1st ed. New York, NY: John Wiley & Sons, Ltd.10.1002/0470863692Search in Google Scholar

Rusnak, M., T.Havranek, and R.Horvath. 2013. “How to Solve the Price Puzzle? A Meta Analysis.” Journal of Money, Credit and Banking45: 37–70.10.1111/j.1538-4616.2012.00561.xSearch in Google Scholar

Sargent, T., and P.Surico. 2011. “Two Illustrations of the Quantity Theory of Money: Breakdowns and Revivals.” American Economic Review101: 109–128.10.1257/aer.101.1.109Search in Google Scholar

Sims, C. A. 1992. “Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy.” European Economic Review36: 975–1000.10.1016/0014-2921(92)90041-TSearch in Google Scholar

Stock, J. H., and M. W.Watson. 1996. “Evidence on Structural Instability in Macroeconomic Time Series Relations.” Journal of Business and Economic Statistics14: 11–30.10.3386/t0164Search in Google Scholar

Stock, J. H., and M. W.Watson. 1998. “Median Unbiased Estimation of Coefficient Variance in a Time-Varying Parameter Model.” Journal of the American Statistical Association93: 349–358.10.3386/t0201Search in Google Scholar

Stock, J. H., and M. W.Watson. 2007. “Why Has US Inflation Become Harder to Forecast?” Journal of Money, Credit and Banking39: 3–33.10.1111/j.1538-4616.2007.00014.xSearch in Google Scholar

Stock, J. H., and M. W.Watson. 2010. “Modeling Inflation After the Crisis.”Working Paper 16488. National Bureau of Economic Research. URL http://www.nber.org/papers/w16488.10.3386/w16488Search in Google Scholar

Tillmann, P. 2009. “The Time-Varying Cost Channel of Monetary Transmission.” Journal of International Money and Finance28: 941–953.10.1016/j.jimonfin.2008.10.003Search in Google Scholar

Watson, M. W. 2014. “Inflation Persistence, the NAIRU, and the Great Recession.” American Economic Review104: 31–36.10.1257/aer.104.5.31Search in Google Scholar

Wu, J. C., and F. D.Xia. 2014. “Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound.”NBER Working Papers 20117. National Bureau of Economic Research, Inc. URL http://ideas.repec.org/p/nbr/nberwo/20117.html.10.3386/w20117Search in Google Scholar

Supplemental Material

The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/snde-2015-0018).

Published Online: 2017-9-4

©2017 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Nonstationary autoregressive conditional duration models
  2. Detecting time variation in the price puzzle: a less informative prior choice for time varying parameter VAR models
  3. The reaction of stock market returns to unemployment
  4. Using the hybrid Phillips curve with memory to forecast US inflation
  5. Time-varying persistence of inflation: evidence from a wavelet-based approach
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https://doi.org/10.1515/snde-2015-0018
Keywords for this article
inverse Wishart prior; Monte Carlo simulation; price puzzle; time varying parameter; vector autoregression

Articles in the same Issue

  1. Nonstationary autoregressive conditional duration models
  2. Detecting time variation in the price puzzle: a less informative prior choice for time varying parameter VAR models
  3. The reaction of stock market returns to unemployment
  4. Using the hybrid Phillips curve with memory to forecast US inflation
  5. Time-varying persistence of inflation: evidence from a wavelet-based approach
  6. Asymmetric exchange rate exposure of stock returns: empirical evidence from Chinese industries
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