[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cui/wpaper/0026.html
   My bibliography  Save this paper

Predicting US CPI-Inflation in the presence of asymmetries, persistence, endogeneity, and conditional heteroscedasticity

Author

Listed:
  • Afees A. Salisu

    (Centre for Econometric and Allied Research, University of Ibadan)

  • Kazeem Isah

    (Centre for Econometric and Allied Research, University of Ibadan)

Abstract
In this paper, we construct a multi-predictor framework for US inflation by augmenting the traditional Phillips curve-based inflation model with symmetric and asymmetric oil price changes. We show that the underlying predictors of US inflation exhibit persistence, endogeneity and conditional heteroscedasticity effects which have implications on forecast performance. Thus, we employ the Westerlund and Narayan (WN hereafter) (2014) estimator which allows for these effects in the predictive model. Also, we follow the linear multi-predictor set-up by Makin et al. (2014) which is an extension of the bivariate predictive model of WN (2014). Thereafter, we extend the former in order to construct a nonlinear multi-predictor model that allows for asymmetries based on Shin et al. (2014) approach. Using historical quarterly data for relevant variables ranging from 1957 to 2017, we demonstrate that US inflation is better modelled with the proposed multi-predictor model suggesting the significance of oil price in the predictive model for US inflation. In addition, we find that the US inflation forecast is episodic and asymmetric. Among the competing multi-predictor variants, the positive oil price-based variant outperforms all other variants both for in-sample and out-of-sample forecasts. The proposed model also outperforms the autoregressive process for a longer out-of-sample period. Our results are robust to different measures of inflation, multiple in-sample periods and forecast horizon.

Suggested Citation

  • Afees A. Salisu & Kazeem Isah, 2017. "Predicting US CPI-Inflation in the presence of asymmetries, persistence, endogeneity, and conditional heteroscedasticity," Working Papers 026, Centre for Econometric and Allied Research, University of Ibadan.
    • Handle: RePEc:cui:wpaper:0026
    as

    Download full text from publisher

    File URL: http://cear.org.ng/index.php?option=com_docman&task=doc_download&gid=65&Itemid=29
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Orphanides, Athanasios & van Norden, Simon, 2005. "The Reliability of Inflation Forecasts Based on Output Gap Estimates in Real Time," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 583-601, June.
    2. Hoang, Thi Hong Van & Lahiani, Amine & Heller, David, 2016. "Is gold a hedge against inflation? New evidence from a nonlinear ARDL approach," Economic Modelling, Elsevier, vol. 54(C), pages 54-66.
    3. Altavilla, Carlo & Ciccarelli, Matteo, 2010. "Evaluating the effect of monetary policy on unemployment with alternative inflation forecasts," Economic Modelling, Elsevier, vol. 27(1), pages 237-253, January.
    4. James H. Stock & Mark W. Watson, 2008. "Phillips curve inflation forecasts," Conference Series ; [Proceedings], Federal Reserve Bank of Boston.
    5. Kilian, Lutz & Vigfusson, Robert J., 2011. "Nonlinearities In The Oil Price–Output Relationship," Macroeconomic Dynamics, Cambridge University Press, vol. 15(S3), pages 337-363, November.
    6. Ahmad, A.H. & Moran Hernandez, Ricardo, 2013. "Asymmetric adjustment between oil prices and exchange rates: Empirical evidence from major oil producers and consumers," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 27(C), pages 306-317.
    7. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    8. Canova, Fabio, 2007. "G-7 Inflation Forecasts: Random Walk, Phillips Curve Or What Else?," Macroeconomic Dynamics, Cambridge University Press, vol. 11(1), pages 1-30, February.
    9. Morana, Claudio, 2017. "Macroeconomic and financial effects of oil price shocks: Evidence for the euro area," Economic Modelling, Elsevier, vol. 64(C), pages 82-96.
    10. Bashar, Omar H.M.N. & Wadud, I.K.M. Mokhtarul & Ali Ahmed, Huson Joher, 2013. "Oil price uncertainty, monetary policy and the macroeconomy: The Canadian perspective," Economic Modelling, Elsevier, vol. 35(C), pages 249-259.
    11. Olivier Coibion & Yuriy Gorodnichenko, 2015. "Is the Phillips Curve Alive and Well after All? Inflation Expectations and the Missing Disinflation," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 197-232, January.
    12. Koop, Gary & Korobilis, Dimitris, 2011. "UK macroeconomic forecasting with many predictors: Which models forecast best and when do they do so?," Economic Modelling, Elsevier, vol. 28(5), pages 2307-2318, September.
    13. Chen, Yu-chin & Turnovsky, Stephen J. & Zivot, Eric, 2014. "Forecasting inflation using commodity price aggregates," Journal of Econometrics, Elsevier, vol. 183(1), pages 117-134.
    14. Christiane Baumeister & Lutz Kilian, 2014. "Do oil price increases cause higher food prices? [Biofuels, binding constraints, and agricultural commodity price volatility]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 29(80), pages 691-747.
    15. LeBlanc, Michael & Chinn, Menzie David, 2004. "Do High Oil Prices Presage Inflation? The Evidence from G-5 Countries," Santa Cruz Department of Economics, Working Paper Series qt4wt4m7hg, Department of Economics, UC Santa Cruz.
    16. Nigel Pain & Isabell Koske & Marte Sollie, 2008. "Globalisation and OECD consumer price inflation," OECD Journal: Economic Studies, OECD Publishing, vol. 2008(1), pages 1-32.
    17. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
    18. Nazlioglu, Saban & Soytas, Ugur, 2011. "World oil prices and agricultural commodity prices: Evidence from an emerging market," Energy Economics, Elsevier, vol. 33(3), pages 488-496, May.
    19. Ascari, Guido, 2000. "Optimising Agents, Staggered Wages and Persistence in the Real Effects of Money Shocks," Economic Journal, Royal Economic Society, vol. 110(465), pages 664-686, July.
    20. Öğünç, Fethi & Akdoğan, Kurmaş & Başer, Selen & Chadwick, Meltem Gülenay & Ertuğ, Dilara & Hülagü, Timur & Kösem, Sevim & Özmen, Mustafa Utku & Tekatlı, Necati, 2013. "Short-term inflation forecasting models for Turkey and a forecast combination analysis," Economic Modelling, Elsevier, vol. 33(C), pages 312-325.
    21. Ji, Qiang & Fan, Ying, 2016. "How do China's oil markets affect other commodity markets both domestically and internationally?," Finance Research Letters, Elsevier, vol. 19(C), pages 247-254.
    22. Capistrán, Carlos & Constandse, Christian & Ramos-Francia, Manuel, 2010. "Multi-horizon inflation forecasts using disaggregated data," Economic Modelling, Elsevier, vol. 27(3), pages 666-677, May.
    23. G. Ascari & E. Marrocu, 2003. "Forecasting inflation: a comparison of linear Phillips curve models and nonlinear time serie models," Working Paper CRENoS 200307, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    24. Makin, Anthony J. & Narayan, Paresh Kumar & Narayan, Seema, 2014. "What expenditure does Anglosphere foreign borrowing fund?," Journal of International Money and Finance, Elsevier, vol. 40(C), pages 63-78.
    25. Lukas Vogel & Elena Rusticelli & Pete Richardson & Stéphanie Guichard & Christian Gianella, 2009. "Inflation Responses to Recent Shocks: Do G7 Countries Behave Differently?," OECD Economics Department Working Papers 689, OECD Publishing.
    26. Narayan, Paresh Kumar & Liu, Ruipeng, 2015. "A unit root model for trending time-series energy variables," Energy Economics, Elsevier, vol. 50(C), pages 391-402.
    27. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    28. Paresh Kumar Narayan & Stephan Popp, 2010. "A new unit root test with two structural breaks in level and slope at unknown time," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1425-1438.
    29. Prasad Bal, Debi & Narayan Rath, Badri, 2015. "Nonlinear causality between crude oil price and exchange rate: A comparative study of China and India," Energy Economics, Elsevier, vol. 51(C), pages 149-156.
    30. Lutz Kilian & Robert J. Vigfusson, 2013. "Do Oil Prices Help Forecast U.S. Real GDP? The Role of Nonlinearities and Asymmetries," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 78-93, January.
    31. Hooker, Mark A, 2002. "Are Oil Shocks Inflationary? Asymmetric and Nonlinear Specifications versus Changes in Regime," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(2), pages 540-561, May.
    32. Afees A. Salisu & Umar B. Ndako & Tirimisiyu F. Oloko & Lateef O. Akanni, 2016. "Unit root modeling for trending stock market series," Borsa Istanbul Review, Research and Business Development Department, Borsa Istanbul, vol. 16(2), pages 82-91, June.
    33. Ang, Andrew & Bekaert, Geert & Wei, Min, 2007. "Do macro variables, asset markets, or surveys forecast inflation better?," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1163-1212, May.
    34. Narayan, Paresh Kumar & Gupta, Rangan, 2015. "Has oil price predicted stock returns for over a century?," Energy Economics, Elsevier, vol. 48(C), pages 18-23.
    35. Nusair, Salah A., 2016. "The effects of oil price shocks on the economies of the Gulf Co-operation Council countries: Nonlinear analysis," Energy Policy, Elsevier, vol. 91(C), pages 256-267.
    36. Robert J. Gordon, 2013. "The Phillips Curve is Alive and Well: Inflation and the NAIRU During the Slow Recovery," NBER Working Papers 19390, National Bureau of Economic Research, Inc.
    37. Dedeoğlu, Dinçer & Kaya, Hüseyin, 2014. "Pass-through of oil prices to domestic prices: Evidence from an oil-hungry but oil-poor emerging market," Economic Modelling, Elsevier, vol. 43(C), pages 67-74.
    38. Martín-Barragán, Belén & Ramos, Sofia B. & Veiga, Helena, 2015. "Correlations between oil and stock markets: A wavelet-based approach," Economic Modelling, Elsevier, vol. 50(C), pages 212-227.
    39. Jiang, Jiaqi & Gu, Rongbao, 2016. "Asymmetrical long-run dependence between oil price and US dollar exchange rate—Based on structural oil shocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 75-89.
    40. Chen, Shiu-Sheng, 2009. "Oil price pass-through into inflation," Energy Economics, Elsevier, vol. 31(1), pages 126-133, January.
    41. Rafiq, Shuddhasattwa & Bloch, Harry, 2016. "Explaining commodity prices through asymmetric oil shocks: Evidence from nonlinear models," Resources Policy, Elsevier, vol. 50(C), pages 34-48.
    42. Kichian, Maral & Rumler, Fabio, 2014. "Forecasting Canadian inflation: A semi-structural NKPC approach," Economic Modelling, Elsevier, vol. 43(C), pages 183-191.
    43. Atems, Bebonchu & Kapper, Devin & Lam, Eddery, 2015. "Do exchange rates respond asymmetrically to shocks in the crude oil market?," Energy Economics, Elsevier, vol. 49(C), pages 227-238.
    44. Marek Rusnak & Tomas Havranek & Roman Horvath, 2013. "How to Solve the Price Puzzle? A Meta‐Analysis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(1), pages 37-70, February.
    45. John Y. Campbell & Samuel B. Thompson, 2008. "Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1509-1531, July.
    46. Phan, Dinh Hoang Bach & Sharma, Susan Sunila & Narayan, Paresh Kumar, 2015. "Stock return forecasting: Some new evidence," International Review of Financial Analysis, Elsevier, vol. 40(C), pages 38-51.
    47. Salisu, Afees A. & Isah, Kazeem O., 2017. "Revisiting the oil price and stock market nexus: A nonlinear Panel ARDL approach," Economic Modelling, Elsevier, vol. 66(C), pages 258-271.
    48. Narayan, Paresh Kumar & Bannigidadmath, Deepa, 2015. "Are Indian stock returns predictable?," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 506-531.
    49. Thi Hong Van Hoang & Amine Lahiani & David Heller, 2016. "Is gold a hedge against inflation? New evidence from a nonlinear ARDL approach," Post-Print hal-02012307, HAL.
    50. McAdam, Peter & McNelis, Paul, 2005. "Forecasting inflation with thick models and neural networks," Economic Modelling, Elsevier, vol. 22(5), pages 848-867, September.
    51. Kuo-Wei Chou & Po-Chun Lin, 2013. "Oil price shocks and producer prices in Taiwan: an application of non-linear error-correction models," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 11(1), pages 59-72, February.
    52. Sek, Siok Kun, 2017. "Impact of oil price changes on domestic price inflation at disaggregated levels: Evidence from linear and nonlinear ARDL modeling," Energy, Elsevier, vol. 130(C), pages 204-217.
    53. James H. Stock & Mark W. Watson, 2010. "Modeling inflation after the crisis," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 173-220.
    54. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    55. Ramos S. & Martin-Barragan B. & Veigad H., 2015. "Correlations between oil and stock markets: A wavelet-based approach," Post-Print hal-01220720, HAL.
    56. Deepa & Paresh K Narayan, "undated". "Are Indian Stock Returns Predictable?," Working Papers 2015_07, Deakin University, Department of Economics.
    57. Sharma, Susan Sunila, 2016. "Can consumer price index predict gold price returns?," Economic Modelling, Elsevier, vol. 55(C), pages 269-278.
    58. Salisu, Afees A. & Adeleke, Adegoke I., 2016. "Further application of Narayan and Liu (2015) unit root model for trending time series," Economic Modelling, Elsevier, vol. 55(C), pages 305-314.
    59. Bec, Frédérique & De Gaye, Annabelle, 2016. "How do oil price forecast errors impact inflation forecast errors? An empirical analysis from US, French and UK inflation forecasts," Economic Modelling, Elsevier, vol. 53(C), pages 75-88.
    60. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
    61. Narayan, Paresh Kumar & Sharma, Susan Sunila, 2014. "Firm return volatility and economic gains: The role of oil prices," Economic Modelling, Elsevier, vol. 38(C), pages 142-151.
    62. Salisu, Afees A. & Oloko, Tirimisiyu F., 2015. "Modeling oil price–US stock nexus: A VARMA–BEKK–AGARCH approach," Energy Economics, Elsevier, vol. 50(C), pages 1-12.
    63. Paresh Kumar Narayan & Stephan Popp, 2013. "Size and power properties of structural break unit root tests," Applied Economics, Taylor & Francis Journals, vol. 45(6), pages 721-728, February.
    64. Nazlioglu, Saban, 2011. "World oil and agricultural commodity prices: Evidence from nonlinear causality," Energy Policy, Elsevier, vol. 39(5), pages 2935-2943, May.
    65. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    66. Christopher J. Neely, 2015. "How Much Do Oil Prices Affect Inflation?," Economic Synopses, Federal Reserve Bank of St. Louis, issue 10.
    67. Sam Olofin & Afees A. Salisu, 2017. "Modelling oil price-inflation nexus: The role of asymmetries and structural breaks," Working Papers 020, Centre for Econometric and Allied Research, University of Ibadan.
    68. Ibarra, Raul, 2012. "Do disaggregated CPI data improve the accuracy of inflation forecasts?," Economic Modelling, Elsevier, vol. 29(4), pages 1305-1313.
    69. Salisu, Afees A. & Isah, Kazeem O. & Oyewole, Oluwatomisin J. & Akanni, Lateef O., 2017. "Modelling oil price-inflation nexus: The role of asymmetries," Energy, Elsevier, vol. 125(C), pages 97-106.
    70. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Salisu, Afees A. & Isah, Kazeem O., 2018. "Predicting US inflation: Evidence from a new approach," Economic Modelling, Elsevier, vol. 71(C), pages 134-158.
    2. Moses Tule & Afees Salisu & Charles Chiemeke, 2020. "Improving Nigeria’s Inflation Forecast with Oil Price: The Role of Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(1), pages 191-229, March.
    3. Moses Tule & Afees A. Salisu & Charles Chimeke, 2018. "You are what you eat: The role of oil price in Nigeria inflation forecast," Working Papers 040, Centre for Econometric and Allied Research, University of Ibadan.
    4. Salisu, Afees A. & Ademuyiwa, Idris & Isah, Kazeem O., 2018. "Revisiting the forecasting accuracy of Phillips curve: The role of oil price," Energy Economics, Elsevier, vol. 70(C), pages 334-356.
    5. Afees A. Salisu & Kazeem O. Isah & Idris Ademuyiwa, 2017. "Testing for asymmetries in the predictive model for oil price-inflation nexus," Economics Bulletin, AccessEcon, vol. 37(3), pages 1797-1804.
    6. Tule, Moses K. & Salisu, Afees A. & Chiemeke, Charles C., 2019. "Can agricultural commodity prices predict Nigeria's inflation?," Journal of Commodity Markets, Elsevier, vol. 16(C).
    7. Salisu, Afees A. & Adekunle, Wasiu & Alimi, Wasiu A. & Emmanuel, Zachariah, 2019. "Predicting exchange rate with commodity prices: New evidence from Westerlund and Narayan (2015) estimator with structural breaks and asymmetries," Resources Policy, Elsevier, vol. 62(C), pages 33-56.
    8. Salisu, Afees A. & Swaray, Raymond & Oloko, Tirimisiyu F., 2019. "Improving the predictability of the oil–US stock nexus: The role of macroeconomic variables," Economic Modelling, Elsevier, vol. 76(C), pages 153-171.
    9. Salisu, Afees A. & Ndako, Umar B. & Oloko, Tirimisiyu F., 2019. "Assessing the inflation hedging of gold and palladium in OECD countries," Resources Policy, Elsevier, vol. 62(C), pages 357-377.
    10. Kazeem O. Isah & Abdulkader C. Mahomedy & Elias A. Udeaja & Ojo J. Adelakun & Yusuf Yakubu & Danmecca Musa, 2022. "Revisiting the accuracy of inflation forecasts in Nigeria: The oil price–exchange rate–asymmetry perspectives," South African Journal of Economics, Economic Society of South Africa, vol. 90(3), pages 329-348, September.
    11. Salisu, Afees A. & Raheem, Ibrahim D. & Ndako, Umar B., 2020. "The inflation hedging properties of gold, stocks and real estate: A comparative analysis," Resources Policy, Elsevier, vol. 66(C).
    12. Salisu, Afees A. & Ogbonna, Ahamuefula E., 2019. "Another look at the energy-growth nexus: New insights from MIDAS regressions," Energy, Elsevier, vol. 174(C), pages 69-84.
    13. Salisu, Afees A. & Isah, Kazeem & Akanni, Lateef O., 2019. "Improving the predictability of stock returns with Bitcoin prices," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 857-867.
    14. Salisu, Afees A. & Isah, Kazeem O. & Raheem, Ibrahim D., 2019. "Testing the predictability of commodity prices in stock returns of G7 countries: Evidence from a new approach," Resources Policy, Elsevier, vol. 64(C).
    15. Afees A. Salisu & Raymond Swaray & Idris Adediran, 2018. "Improving the predictability of commodity prices in US inflation: The role of coffee price," Working Papers 041, Centre for Econometric and Allied Research, University of Ibadan.
    16. Sarwar, Muhammad Nadeem & Hussain, Hamid & Maqbool, Muhammad Bilal, 2020. "Pass through effects of oil price on food and non-food prices in Pakistan: A nonlinear ARDL approach," Resources Policy, Elsevier, vol. 69(C).
    17. Raheem, Ibrahim & Olabisi, Nafisat, 2019. "What is new? The role of asymmetry and breaks in oil price–output growth volatility nexus," MPRA Paper 105361, University Library of Munich, Germany.
    18. Fasanya, Ismail O. & Awodimila, Crystal P., 2020. "Are commodity prices good predictors of inflation? The African perspective," Resources Policy, Elsevier, vol. 69(C).
    19. Salisu, Afees A. & Isah, Kazeem O., 2017. "Revisiting the oil price and stock market nexus: A nonlinear Panel ARDL approach," Economic Modelling, Elsevier, vol. 66(C), pages 258-271.
    20. Sun, Qingru & An, Haizhong & Gao, Xiangyun & Guo, Sui & Wang, Ze & Liu, Siyao & Wen, Shaobo, 2019. "Effects of crude oil shocks on the PPI system based on variance decomposition network analysis," Energy, Elsevier, vol. 189(C).

    More about this item

    Keywords

    OECD; Phillips curve; Asymmetries; Inflation forecasts; Forecast evaluation;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cui:wpaper:0026. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Adeoye Omosebi (email available below). General contact details of provider: https://edirc.repec.org/data/ceuibng.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.