IDEAS home Printed from https://ideas.repec.org/p/esx/essedp/5757.html
   My bibliography  Save this paper

Regression towards the mode

Author

Listed:
  • Kemp, GCR
  • Santos Silva, JMC

Abstract

We propose a semi-parametric mode regression estimator for the case in which the variate of interest is continuous and observable over its entire un- bounded support. The estimator is semi-parametric in that the conditional mode is specified as a parametric function, but only mild assumptions are made about the nature of the conditional density of interest. We show that the proposed estimator is consistent and has a tractable asymptotic distribution. Simulation results and an empirical illustration are provided to highlight the practicality and usefulness of the estimator.

Suggested Citation

  • Kemp, GCR & Santos Silva, JMC, 2010. "Regression towards the mode," Economics Discussion Papers 5757, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:5757
    as

    Download full text from publisher

    File URL: https://repository.essex.ac.uk/5757/
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Lee, Myoung-jae, 1989. "Mode regression," Journal of Econometrics, Elsevier, vol. 42(3), pages 337-349, November.
    3. A. Quintela-Del-Río & Ph. Vieu, 1997. "A nonparametric conditional mode estimate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 8(3), pages 253-266, September.
    4. Manski, Charles F, 1991. "Regression," Journal of Economic Literature, American Economic Association, vol. 29(1), pages 34-50, March.
    5. Bound, John & Krueger, Alan B, 1991. "The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right?," Journal of Labor Economics, University of Chicago Press, vol. 9(1), pages 1-24, January.
    6. Lee, Myoung-jae, 1993. "Quadratic mode regression," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 1-19.
    7. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    8. David M. Cutler & Edward L. Glaeser & Jesse M. Shapiro, 2003. "Why Have Americans Become More Obese?," Journal of Economic Perspectives, American Economic Association, vol. 17(3), pages 93-118, Summer.
    9. Terence C. Mills, 2009. "Forecasting obesity trends in England," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 107-117, January.
    10. Chou, Shin-Yi & Grossman, Michael & Saffer, Henry, 2004. "An economic analysis of adult obesity: results from the Behavioral Risk Factor Surveillance System," Journal of Health Economics, Elsevier, vol. 23(3), pages 565-587, May.
    11. Ferraty, Frederic & Quintela-del-Río, Alejandro & Vieu, Philippe, 2012. "Specification Test For Conditional Distribution With Functional Data," Econometric Theory, Cambridge University Press, vol. 28(2), pages 363-386, April.
    12. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    13. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    14. Hansen, Bruce E., 1996. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 12(2), pages 347-359, June.
    15. John Cawley, 2004. "The Impact of Obesity on Wages," Journal of Human Resources, University of Wisconsin Press, vol. 39(2).
    16. Jonathan R. W. Temple, 1998. "Robustness tests of the augmented Solow model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 361-375.
    17. Baldauf, Markus & Santos Silva, J.M.C., 2012. "On the use of robust regression in econometrics," Economics Letters, Elsevier, vol. 114(1), pages 124-127.
    18. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    19. Chesher, Andrew & Peters, Simon, 1994. "Symmetry, Regression Design, and Sampling Distributions," Econometric Theory, Cambridge University Press, vol. 10(1), pages 116-129, March.
    20. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    21. repec:sae:niesru:v:167:y::i:1:p:106-112 is not listed on IDEAS
    22. Pedro S. Martins & Gary Solon & Jonathan Thomas, 2010. "Measuring What Employers Really Do about Entry Wages over the Business Cycle," NBER Working Papers 15767, National Bureau of Economic Research, Inc.
    23. M'hamed Ezzahrioui & Elias Ould Saïd, 2010. "Some asymptotic results of a non‐parametric conditional mode estimator for functional time‐series data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 171-201, May.
    24. Ana Rute Cardoso & Pedro Portugal, 2005. "Contractual Wages and the Wage Cushion under Different Bargaining Settings," Journal of Labor Economics, University of Chicago Press, vol. 23(4), pages 875-902, October.
    25. Jonathan Temple, 1999. "The New Growth Evidence," Journal of Economic Literature, American Economic Association, vol. 37(1), pages 112-156, March.
    26. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    27. Kenneth F. Wallis, 1999. "Asymmetric density forecasts of inflation and the Bank of England's fan chart," National Institute Economic Review, National Institute of Economic and Social Research, vol. 167(1), pages 106-112, January.
    28. M.‐J. Lee & H. Kim, 1998. "Semiparametric econometric estimators for a truncated regression model: a review with an extension," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(2), pages 200-225, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Timo Dimitriadis & Andrew J. Patton & Patrick W. Schmidt, 2019. "Testing Forecast Rationality for Measures of Central Tendency," Papers 1910.12545, arXiv.org, revised Jun 2023.
    2. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    3. Gordon C. R. Kemp & Paulo M. D. C. Parente & J. M. C. Santos Silva, 2020. "Dynamic Vector Mode Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 647-661, July.
    4. Jales, Hugo & Jiang, Boqian & Rosenthal, Stuart S., 2023. "JUE Insight: Using the mode to test for selection in city size wage premia," Journal of Urban Economics, Elsevier, vol. 133(C).
    5. Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    6. Yen-Chi Chen, 2017. "Modal Regression using Kernel Density Estimation: a Review," Papers 1710.07004, arXiv.org, revised Dec 2017.
    7. Baldauf, Markus & Santos Silva, J.M.C., 2012. "On the use of robust regression in econometrics," Economics Letters, Elsevier, vol. 114(1), pages 124-127.
    8. Lv, Zhike & Zhu, Huiming & Yu, Keming, 2014. "Robust variable selection for nonlinear models with diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 90-97.
    9. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    10. Hyun Kim & Yong-seong Kim & Myoung-jae Lee, 2012. "Treatment effect analysis of early reemployment bonus program: panel MLE and mode-based semiparametric estimator for interval truncation," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 11(3), pages 189-209, December.
    11. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    12. Weixin Yao & Longhai Li, 2014. "Acknowledgement of Priority," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1195-1195, December.
    13. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    14. Gianni Cicia & Marilena Furno & Teresa Giudice, 2021. "Do consumers’ values and attitudes affect food retailer choice? Evidence from a national survey on farmers’ market in Germany," Agricultural and Food Economics, Springer;Italian Society of Agricultural Economics (SIDEA), vol. 9(1), pages 1-21, December.
    15. repec:esx:essedp:761 is not listed on IDEAS
    16. Shi, Jianhong & Zhang, Yujing & Yu, Ping & Song, Weixing, 2021. "SIMEX estimation in parametric modal regression with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    17. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2022. "Characterizing M-estimators," Papers 2208.08108, arXiv.org.

    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. Baldauf, Markus & Santos Silva, J.M.C., 2012. "On the use of robust regression in econometrics," Economics Letters, Elsevier, vol. 114(1), pages 124-127.
    2. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    3. Costa-Font, Joan & Fabbri, Daniele & Gil, Joan, 2009. "Decomposing body mass index gaps between Mediterranean countries: A counterfactual quantile regression analysis," Economics & Human Biology, Elsevier, vol. 7(3), pages 351-365, December.
    4. Vincenzo Atella & Joanna Kopinska, 2011. "Body weight of Italians: the weight of Education," CEIS Research Paper 189, Tor Vergata University, CEIS, revised 23 Mar 2011.
    5. García Villar, Jaume & Quintana-Domeque, Climent, 2009. "Income and body mass index in Europe," Economics & Human Biology, Elsevier, vol. 7(1), pages 73-83, March.
    6. Yen-Chi Chen, 2017. "Modal Regression using Kernel Density Estimation: a Review," Papers 1710.07004, arXiv.org, revised Dec 2017.
    7. Boizot-Szantai, Christine & Etile, Fabrice, 2005. "The Food Prices / Body Mass Index Relationship: Theory and Evidence from a Sample of French Adults," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24734, European Association of Agricultural Economists.
    8. Michael S. Delgado & Daniel J. Henderson & Christopher F. Parmeter, 2014. "Does Education Matter for Economic Growth?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 334-359, June.
    9. Euna Han & Lisa M. Powell, 2013. "Fast Food Prices And Adult Body Weight Outcomes: Evidence Based On Longitudinal Quantile Regression Models," Contemporary Economic Policy, Western Economic Association International, vol. 31(3), pages 528-536, July.
    10. Baum II, Charles L. & Ruhm, Christopher J., 2009. "Age, socioeconomic status and obesity growth," Journal of Health Economics, Elsevier, vol. 28(3), pages 635-648, May.
    11. David G. Blanchflower & Andrew J. Oswald & Bert Van Landeghem, 2009. "Imitative Obesity and Relative Utility," Journal of the European Economic Association, MIT Press, vol. 7(2-3), pages 528-538, 04-05.
    12. Stifel, David C. & Averett, Susan L., 2009. "Childhood overweight in the United States: A quantile regression approach," Economics & Human Biology, Elsevier, vol. 7(3), pages 387-397, December.
    13. Pierre Dubois & Rachel Griffith & Aviv Nevo, 2014. "Do Prices and Attributes Explain International Differences in Food Purchases?," American Economic Review, American Economic Association, vol. 104(3), pages 832-867, March.
    14. Sarah Brown & William Greene & Mark Harris, 2020. "A novel approach to latent class modelling: identifying the various types of body mass index individuals," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 983-1004, June.
    15. Adriana Barone & Cristian Barra, 2022. "Weight Status and Depression in Italy: Evidence from the Second Wave of the European Health Interview Survey," Journal of Interdisciplinary Economics, , vol. 34(2), pages 193-227, July.
    16. Charles J. Courtemanche & Joshua C. Pinkston & Christopher J. Ruhm & George L. Wehby, 2016. "Can Changing Economic Factors Explain the Rise in Obesity?," Southern Economic Journal, John Wiley & Sons, vol. 82(4), pages 1266-1310, April.
    17. Tafreschi, Darjusch, 2015. "The income body weight gradients in the developing economy of China," Economics & Human Biology, Elsevier, vol. 16(C), pages 115-134.
    18. Pieroni, Luca & Salmasi, Luca, 2010. "Body weight and socio-economic determinants: quantile estimations from the British Household Panel Survey," ISER Working Paper Series 2010-41, Institute for Social and Economic Research.
    19. Oswald, Andrew J & Powdthavee, Nattavudh, 2007. "Obesity, Unhappiness, and The Challenge of Affluence : Theory and Evidence," The Warwick Economics Research Paper Series (TWERPS) 793, University of Warwick, Department of Economics.
    20. Maximilian D. Schmeiser, 2009. "Expanding wallets and waistlines: the impact of family income on the BMI of women and men eligible for the Earned Income Tax Credit," Health Economics, John Wiley & Sons, Ltd., vol. 18(11), pages 1277-1294, November.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    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:esx:essedp:5757. 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: Essex Economics Web Manager (email available below). General contact details of provider: https://edirc.repec.org/data/edessuk.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.